Spectral Measures and Dynamics: Typical Behaviors (1st ed. 2023) (Latin American Mathematics Series)

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Synopsis
This book convenes and deepens generic results about spectral measures, many of them available so far in scattered literature. It starts with classic topics such as Wiener lemma, Strichartz inequality, and the basics of fractal dimensions of measures, progressing to more advanced material, some of them developed by the own authors.A fundamental concept to the mathematical theory of quantum mechanics, the spectral measure relates to the components of the quantum state concerning the energy levels of the Hamiltonian operator and, on the other hand, to the dynamics of such state. However, these correspondences are not immediate, with many nuances and subtleties discovered in recent years.A valuable example of such subtleties is found in the so-called “Wonderland theorem” first published by B. Simon in 1995. It shows that, for some metric space of self-adjoint operators, the set of operators whose spectral measures are singular continuous is a generic set (which, for some, is exotic). Recent works have revealed that, on top of singular continuity, there are other generic properties of spectral measures. These properties are usually associated with a number of different notions of generalized dimensions, upper and lower dimensions, with dynamical implications in quantum mechanics, ergodicity of dynamical systems, and evolution semigroups. All this opens ways to new and instigating avenues of research.Graduate students with a specific interest in the spectral properties of spectral measure are the primary target audience for this work, while researchers benefit from a selection of important results, many of them presented in the book format for the first time.
Copyright:
2023

Book Details

Book Quality:
Publisher Quality
ISBN-13:
9783031382895
Related ISBNs:
9783031382888
Publisher:
Springer International Publishing
Date of Addition:
Copyrighted By:
The Editor
Adult content:
No
Language:
English
Has Image Descriptions:
No
Categories:
Nonfiction, Science, Earth Sciences, Mathematics and Statistics
Submitted By:
Bookshare Staff
Usage Restrictions:
This is a copyrighted book.

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