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Function Spaces: The Fifth Conference (Lecture Notes in Pure and Applied Mathematics)
by Henryk Hudzik Leszek SkrzypczakThis volume compiles research results from the fifth Function Spaces International Conference, held in Poznan, Poland. It presents key advances, modern applications and analyses of function spaces and contains two special sections recognizing the contributions and influence of Wladyslaw Orlicz and Genadil Lozanowskii.
Function Theory on Planar Domains: A Second Course in Complex Analysis
by Stephen D. FisherA high-level treatment of complex analysis, this text focuses on function theory on a finitely connected planar domain. Clear and complete, it emphasizes domains bounded by a finite number of disjoint analytic simple closed curves.The first chapter and parts of Chapters 2 and 3 offer background material, all of it classical and important in its own right. The remainder of the text presents results in complex analysis from the far, middle, and recent past, all selected for their interest and merit as substantive mathematics. Suitable for upper-level undergraduates and graduate students, this text is accessible to anyone with a background in complex and functional analysis. Author Stephen D. Fisher, a professor of mathematics at Northwestern University, elaborates upon and extends results with a set of exercises at the end of each chapter.
Functional Analysis
by Béla Sz. Nagy Frigyes RieszClassic exposition of modern theories of differentiation and integration and principal problems and methods of handling integral equations and linear functionals and transformations. 1955 edition.
Functional Analysis
by Lawrence Narici George BachmanExcellent treatment of the subject geared toward students with background in linear algebra, advanced calculus, physics and engineering. Text covers introduction to inner-product spaces, normed and metric spaces, and topological spaces; complete orthonormal sets, the Hahn-Banach theorem and its consequences, spectral notions, square roots, a spectral decomposition theorem, and many other related subjects. Chapters conclude with exercises intended to test and reinforce reader's understanding of text material. A glossary of definitions, detailed proofs of theorems, bibliography, and index of symbols round out this comprehensive text. 1966 edition.
Functional Analysis
by Joseph MuscatThis textbook is an introduction to functional analysis suited to final year undergraduates or beginning graduates. Its various applications of Hilbert spaces, including least squares approximation, inverse problems, and Tikhonov regularization, should appeal not only to mathematicians interested in applications, but also to researchers in related fields. Functional Analysis adopts a self-contained approach to Banach spaces and operator theory that covers the main topics, based upon the classical sequence and function spaces and their operators. It assumes only a minimum of knowledge in elementary linear algebra and real analysis; the latter is redone in the light of metric spaces. It contains more than a thousand worked examples and exercises, which make up the main body of the book.
Functional Analysis
by Peter D. LaxIncludes sections on the spectral resolution and spectral representation of self adjoint operators, invariant subspaces, strongly continuous one-parameter semigroups, the index of operators, the trace formula of Lidskii, the Fredholm determinant, and more.* Assumes prior knowledge of Naive set theory, linear algebra, point set topology, basic complex variable, and real variables.* Includes an appendix on the Riesz representation theorem.
Functional Analysis Tools for Practical Use in Sciences and Engineering
by Carlos A. de MouraThis textbook describes selected topics in functional analysis as powerful tools of immediate use in many fields within applied mathematics, physics and engineering. It follows a very reader-friendly structure, with the presentation and the level of exposition especially tailored to those who need functional analysis but don’t have a strong background in this branch of mathematics. For every tool, this work emphasizes the motivation, the justification for the choices made, and the right way to employ the techniques. Proofs appear only when necessary for the safe use of the results. The book gently starts with a road map to guide reading. A subsequent chapter recalls definitions and notation for abstract spaces and some function spaces, while Chapter 3 enters dual spaces. Tools from Chapters 2 and 3 find use in Chapter 4, which introduces distributions. The Linear Functional Analysis basic triplet makes up Chapter 5, followed by Chapter 6, which introduces the concept of compactness. Chapter 7 brings a generalization of the concept of derivative for functions defined in normed spaces, while Chapter 8 discusses basic results about Hilbert spaces that are paramount to numerical approximations. The last chapter brings remarks to recent bibliographical items. Elementary examples included throughout the chapters foster understanding and self-study. By making key, complex topics more accessible, this book serves as a valuable resource for researchers, students, and practitioners alike that need to rely on solid functional analysis but don’t need to delve deep into the underlying theory.
Functional Analysis and Applications (Chapman And Hall/crc Research Notes In Mathematics Ser. #377)
by Abul Hasan SiddiqiThis self-contained textbook discusses all major topics in functional analysis. Combining classical materials with new methods, it supplies numerous relevant solved examples and problems and discusses the applications of functional analysis in diverse fields. The book is unique in its scope, and a variety of applications of functional analysis and operator-theoretic methods are devoted to each area of application. Each chapter includes a set of problems, some of which are routine and elementary, and some of which are more advanced. The book is primarily intended as a textbook for graduate and advanced undergraduate students in applied mathematics and engineering. It offers several attractive features making it ideally suited for courses on functional analysis intended to provide a basic introduction to the subject and the impact of functional analysis on applied and computational mathematics, nonlinear functional analysis and optimization. It introduces emerging topics like wavelets, Gabor system, inverse problems and application to signal and image processing.
Functional Analysis and Applications (Industrial and Applied Mathematics #377)
by Abul Hasan SiddiqiThis self-contained textbook discusses all major topics in functional analysis. Combining classical materials with new methods, it supplies numerous relevant solved examples and problems and discusses the applications of functional analysis in diverse fields. The book is unique in its scope, and a variety of applications of functional analysis and operator-theoretic methods are devoted to each area of application. Each chapter includes a set of problems, some of which are routine and elementary, and some of which are more advanced. The book is primarily intended as a textbook for graduate and advanced undergraduate students in applied mathematics and engineering. It offers several attractive features making it ideally suited for courses on functional analysis intended to provide a basic introduction to the subject and the impact of functional analysis on applied and computational mathematics, nonlinear functional analysis and optimization. It introduces emerging topics like wavelets, Gabor system, inverse problems and application to signal and image processing.
Functional Analysis and Applied Optimization in Banach Spaces
by Fabio BotelhoThis book introduces the basic concepts of real and functional analysis. It presents the fundamentals of the calculus of variations, convex analysis, duality, and optimization that are necessary to develop applications to physics and engineering problems. The book includes introductory and advanced concepts in measure and integration, as well as an introduction to Sobolev spaces. The problems presented are nonlinear, with non-convex variational formulation. Notably, the primal global minima may not be attained in some situations, in which cases the solution of the dual problem corresponds to an appropriate weak cluster point of minimizing sequences for the primal one. Indeed, the dual approach more readily facilitates numerical computations for some of the selected models. While intended primarily for applied mathematicians, the text will also be of interest to engineers, physicists, and other researchers in related fields.
Functional Analysis and Continuous Optimization: In Honour of Juan Carlos Ferrando's 65th Birthday, Elche, Spain, June 16–17, 2022 (Springer Proceedings in Mathematics & Statistics #424)
by Manuel López-Pellicer José M. Amigó María J. Cánovas Marco A. López-CerdáThe book includes selected contributions presented at the "International Meeting on Functional Analysis and Continuous Optimization" held in Elche (Spain) on June 16–17, 2022. Its contents cover very recent results in functional analysis, continuous optimization and the interplay between these disciplines. Therefore, this book showcases current research on functional analysis and optimization with individual contributions, as well as new developments in both areas. As a result, the reader will find useful information and stimulating ideas.
Functional Analysis and Operator Algebras (CMS/CAIMS Books in Mathematics #13)
by Kenneth R. DavidsonThis book offers a comprehensive introduction to various aspects of functional analysis and operator algebras. In Part I, readers will find the foundational material suitable for a one-semester course on functional analysis and linear operators. Additionally, Part I includes enrichment topics that provide flexibility for instructors. Part II covers the fundamentals of Banach algebras and C*-algebras, followed by more advanced material on C* and von Neumann algebras. This section is suitable for use in graduate courses, with instructors having the option to select specific topics. Part III explores a range of important topics in operator theory and operator algebras. These include $H^p$ spaces, isometries and Toeplitz operators, nest algebras, dilation theory, applications to various classes of nonself-adjoint operator algebras, and noncommutative convexity and Choquet theory. This material is suitable for graduate courses and learning seminars, offering instructors flexibility in selecting topics.
Functional Analysis and Operator Theory (Problem Books in Mathematics)
by Alexander Kukush Yuliya Mishura Volodymyr Brayman Andrii Chaikovskyi Oleksii Konstantinov Oleksii NesterenkoThe book contains a collection of more than 800 problems from all main chapters of functional analysis, with theoretical background and solutions. It is mostly intended for undergraduate students who are starting to study the course of functional analysis. The book will also be useful for graduate and post- graduate students and researchers who wish to refresh their knowledge and deepen their understanding of the subject, as well as for teachers of functional analysis and related disciplines. It can be used for independent study as well. It is assumed that the reader has mastered standard courses of calculus and measure theory and has basic knowledge of linear algebra, analytic geometry, and differential equations. This collection of problems can help students of different levels of training and different areas of specialization to learn how to solve problems in functional analysis. Each chapter of the book has similar structure and consists of the following sections: Theoretical Background, Examples of Problems with Solutions, and Problems to Solve. The book contains theoretical preliminaries to ensure that the reader understands the statements of problems and is able to successfully solve them. Then examples of typical problems with detailed solutions are included, and this is relevant not only for those students who have significant difficulties in studying this subject, but also for other students who due to various circumstances сcould be deprived of communication with a teacher. There are problems for independent solving, and the corresponding selection of problems reflects all the main plot lines that relate to a given topic. The number of problems is sufficient both for a teacher to give practical lessons, to set homework, to prepare tasks for various forms of control, and for those students who want to study the discipline more deeply. Problems of a computational nature are provided with answers, while theoretical problems, the solutions ofwhich require non-trivial ideas or new techniques, are provided with detailed hints or solutions to introduce the reader to the corresponding ideas or techniques.
Functional Analysis and Optimization Methods in Hadron Physics (SpringerBriefs in Physics)
by Irinel CapriniThis book begins with a brief historical review of the early applications of standard dispersion relations in particle physics. It then presents the modern perspective within the Standard Model, emphasizing the relation of analyticity together with alternative tools applied to strong interactions, such as perturbative and lattice quantum chromodynamics (QCD), as well as chiral perturbation theory. The core of the book argues that, in order to improve the prediction of specific hadronic observables, it is often necessary to resort to methods of complex analysis more sophisticated than the simple Cauchy integral. Accordingly, a separate mathematical chapter is devoted to solving several functional analysis optimization problems. Their applications to physical amplitudes and form factors are discussed in the following chapters, which also demonstrate how to merge the analytic approach with statistical analysis tools. Given its scope, the book offers a valuable guide for researchers working in precision hadronic physics, as well as graduate students who are new to the field.
Functional Analysis and Summability
by P.N. NatarajanThere are excellent books on both functional analysis and summability. Most of them are very terse. In Functional Analysis and Summability, the author makes a sincere attempt for a gentle introduction of these topics to students. In the functional analysis component of the book, the Hahn–Banach theorem, Banach–Steinhaus theorem (or uniform boundedness principle), the open mapping theorem, the closed graph theorem, and the Riesz representation theorem are highlighted. In the summability component of the book, the Silverman–Toeplitz theorem, Schur’s theorem, the Steinhaus theorem, and the Steinhaus-type theorems are proved. The utility of functional analytic tools like the uniform boundedness principle to prove some results in summability theory is also pointed out. Features A gentle introduction of the topics to the students is attempted. Basic results of functional analysis and summability theory and their applications are highlighted. Many examples are provided in the text. Each chapter ends with useful exercises. This book will be useful to postgraduate students, pre-research level students, and research scholars in mathematics. Students of physics and engineering will also find this book useful since topics in the book also have applications in related areas.
Functional Analysis and Valuation Theory (Chapman & Hall/CRC Pure and Applied Mathematics)
by Lawrence NariciThis book presents functional analysis over arbitrary valued fields and investigates normed spaces and algebras over fields with valuation, with attention given to the case when the norm and the valuation are nonarchimedean. It considers vector spaces over fields with nonarchimedean valuation.
Functional Analysis and the Feynman Operator Calculus
by Tepper L. Gill Woodford W. ZacharyThis book provides the mathematical foundations forFeynman's operator calculus and for the Feynman path integral formulation ofquantum mechanics as a natural extension of analysis and functional analysis tothe infinite-dimensional setting. In one application, the resultsare used to prove the last two remaining conjectures of Freeman Dyson forquantum electrodynamics. In another application, the results are used tounify methods and weaken domain requirements for non-autonomous evolutionequations. Other applications include a general theory of Lebesguemeasure on Banach spaces with a Schauder basis and a new approach to thestructure theory of operators on uniformly convex Banach spaces. This book isintended for advanced graduate students and researchers.
Functional Analysis for the Applied Mathematician (Textbooks in Mathematics)
by Todd Arbogast Jerry L. BonaFunctional Analysis for the Applied Mathematician is a self-contained volume providing a rigorous introduction to functional analysis and its applications. Students from mathematics, science, engineering, and certain social science and interdisciplinary programs will benefit from the material. It is accessible to graduate and advanced undergraduate students with a solid background in undergraduate mathematics and an appreciation of mathematical rigor. Students are called upon to actively engage with the material, to the point of proving some of the basic results or their straightforward generalizations, both within the text and within the generous set of exercises.Features: Replete with exercises and examples Suitable for graduate students and advanced undergraduates Develops the basics of functional analysis, exploring the interplay between algebraic linear space theory and topology Presents a variety of applications, often dealing with partial differential equations and their numerical approximation Doubles as a reference book with an extensive index listing the concepts and results
Functional Analysis for the Applied Sciences (Universitext)
by Gheorghe MoroşanuThis advanced graduate textbook presents main results and techniques in Functional Analysis and uses them to explore other areas of mathematics and applications. Special attention is paid to creating appropriate frameworks towards solving significant problems involving differential and integral equations. Exercises at the end of each chapter help the reader to understand the richness of ideas and methods offered by Functional Analysis. Some of the exercises supplement theoretical material, while others relate to the real world. This textbook, with its friendly exposition, focuses on different problems in physics and other applied sciences and uniquely provides solutions to most of the exercises. The text is aimed toward graduate students and researchers in applied mathematics, physics, and neighboring fields of science.
Functional Analysis in Applied Mathematics and Engineering (Studies In Advanced Mathematics Ser. #31)
by Michael PedersenPresenting excellent material for a first course on functional analysis , Functional Analysis in Applied Mathematics and Engineering concentrates on material that will be useful to control engineers from the disciplines of electrical, mechanical, and aerospace engineering.This text/reference discusses:rudimentary topologyBanach's fixed point theorem with applicationsL^p-spacesdensity theorems for testfunctionsinfinite dimensional spacesbounded linear operatorsFourier seriesopen mapping and closed graph theoremscompact and differential operatorsHilbert-Schmidt operatorsVolterra equationsSobolev spacescontrol theory and variational analysisHilbert Uniqueness Methodboundary element methodsFunctional Analysis in Applied Mathematics and Engineering begins with an introduction to the important, abstract basic function spaces and operators with mathematical rigor, then studies problems in the Hilbert space setting. The author proves the spectral theorem for unbounded operators with compact inverses and goes on to present the abstract evolution semigroup theory for time dependent linear partial differential operators. This structure establishes a firm foundation for the more advanced topics discussed later in the text.
Functional Analysis in Interdisciplinary Applications
by Michael V. Ruzhansky Tynysbek Sh. Kalmenov Erlan D. Nursultanov Makhmud A. SadybekovThis volume presents current research in functional analysis and its applications to a variety of problems in mathematics and mathematical physics. The book contains over forty carefully refereed contributions to the conference "Functional Analysis in Interdisciplinary Applications" (Astana, Kazakhstan, October 2017). Topics covered include the theory of functions and functional spaces; differential equations and boundary value problems; the relationship between differential equations, integral operators and spectral theory; and mathematical methods in physical sciences. Presenting a wide range of topics and results, this book will appeal to anyone working in the subject area, including researchers and students interested to learn more about different aspects and applications of functional analysis.
Functional Analysis in Interdisciplinary Applications—II: ICAAM, Lefkosa, Cyprus, September 6–9, 2018 (Springer Proceedings in Mathematics & Statistics #351)
by Michael V. Ruzhansky Tynysbek Sh. Kalmenov Makhmud A. Sadybekov Durvudkhan Suragan Allaberen AshyralyevFunctional analysis is an important branch of mathematical analysis which deals with the transformations of functions and their algebraic and topological properties. Motivated by their large applicability to real life problems, applications of functional analysis have been the aim of an intensive study effort in the last decades, yielding significant progress in the theory of functions and functional spaces, differential and difference equations and boundary value problems, differential and integral operators and spectral theory, and mathematical methods in physical and engineering sciences. The present volume is devoted to these investigations. The publication of this collection of papers is based on the materials of the mini-symposium "Functional Analysis in Interdisciplinary Applications" organized in the framework of the Fourth International Conference on Analysis and Applied Mathematics (ICAAM 2018, September 6–9, 2018). Presenting a wide range of topics and results, this book will appeal to anyone working in the subject area, including researchers and students interested to learn more about different aspects and applications of functional analysis. Many articles are written by experts from around the world, strengthening international integration in the fields covered. The contributions to the volume, all peer reviewed, contain numerous new results.This volume contains four different chapters. The first chapter contains the contributed papers focusing on various aspects of the theory of functions and functional spaces. The second chapter is devoted to the research on difference and differential equations and boundary value problems. The third chapter contains the results of studies on differential and integral operators and on the spectral theory. The fourth chapter is focused on the simulation of problems arising in real-world applications of applied sciences.
Functional Analysis, Calculus of Variations and Numerical Methods for Models in Physics and Engineering
by Fabio Silva BotelhoThe book discusses basic concepts of functional analysis, measure and integration theory, calculus of variations and duality and its applications to variational problems of non-convex nature, such as the Ginzburg-Landau system in superconductivity, shape optimization models, dual variational formulations for micro-magnetism and others. Numerical Methods for such and similar problems, such as models in flight mechanics and the Navier-Stokes system in fluid mechanics have been developed through the generalized method of lines, including their matrix finite dimensional approximations. It concludes with a review of recent research on Riemannian geometry applied to Quantum Mechanics and Relativity. The book will be of interest to applied mathematicians and graduate students in applied mathematics. Physicists, engineers and researchers in related fields will also find the book useful in providing a mathematical background applicable to their respective professional areas.
Functional Analysis, Calculus of Variations and Optimal Control
by Francis ClarkeFunctional analysis owes much of its early impetus to problems that arise in the calculus of variations. In turn, the methods developed there have been applied to optimal control, an area that also requires new tools, such as nonsmooth analysis. This self-contained textbook gives a complete course on all these topics. It is written by a leading specialist who is also a noted expositor. This book provides a thorough introduction to functional analysis and includes many novel elements as well as the standard topics. A short course on nonsmooth analysis and geometry completes the first half of the book whilst the second half concerns the calculus of variations and optimal control. The author provides a comprehensive course on these subjects, from their inception through to the present. A notable feature is the inclusion of recent, unifying developments on regularity, multiplier rules, and the Pontryagin maximum principle, which appear here for the first time in a textbook. Other major themes include existence and Hamilton-Jacobi methods. The many substantial examples, and the more than three hundred exercises, treat such topics as viscosity solutions, nonsmooth Lagrangians, the logarithmic Sobolev inequality, periodic trajectories, and systems theory. They also touch lightly upon several fields of application: mechanics, economics, resources, finance, control engineering. Functional Analysis, Calculus of Variations and Optimal Control is intended to support several different courses at the first-year or second-year graduate level, on functional analysis, on the calculus of variations and optimal control, or on some combination. For this reason, it has been organized with customization in mind. The text also has considerable value as a reference. Besides its advanced results in the calculus of variations and optimal control, its polished presentation of certain other topics (for example convex analysis, measurable selections, metric regularity, and nonsmooth analysis) will be appreciated by researchers in these and related fields.
Functional Analysis, Holomorphy, and Approximation Theory (Lecture Notes In Pure And Applied Mathematics Ser. #83)
by Guido I. ZapataThis book contains papers on complex analysis, function spaces, harmonic analysis, and operators, presented at the International seminar on Functional Analysis, Holomorphy, and Approximation Theory held in 1979. It is addressed to mathematicians and advanced graduate students in mathematics.