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Spectral measures and dynamicstypical behaviors /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Spectral measures and dynamicsby Moacir Aloisio, Silas L. Carvalho, César R. de Oliveira.
Reminder of title:	typical behaviors /
Author:	Aloisio, Moacir.
other author:	Carvalho, Silas L.
Published:	Cham :Springer International Publishing :2023.
Description:	xi, 246 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Spectral theory (Mathematics)
Online resource:	https://doi.org/10.1007/978-3-031-38289-5
ISBN:	9783031382895$q(electronic bk.)

Spectral measures and dynamicstypical behaviors /
Aloisio, Moacir.

Spectral measures and dynamicstypical behaviors /[electronic resource] :by Moacir Aloisio, Silas L. Carvalho, César R. de Oliveira. - Cham :Springer International Publishing :2023. - xi, 246 p. :ill., digital ;24 cm. - Latin American mathematics series - UFSCar subseries,2524-6763. - Latin American mathematics series - UFSCar subseries..

Spectrum and Dynamics: Some Basic Concepts -- Part I Quantum Models: Correlation Dimension -- Fractal Measures and Dynamics -- Escaping Probabilities and Quasiballistic Dynamics -- Generalized Dimensions and Dynamics -- Part II Ergodic Theory and Semigroups: Generic Scales of Weak-Mixing -- Asymptotics of C0-Semigroups -- Generic Stability for Self-adjoint Semigroups -- References.

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.

ISBN: 9783031382895$q(electronic bk.)

Standard No.: 10.1007/978-3-031-38289-5doiSubjects--Topical Terms:

182365
Spectral theory (Mathematics)

LC Class. No.: QA320 / .A46 2023

Dewey Class. No.: 515.7222

Spectral measures and dynamicstypical behaviors /
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245 1 0 $a Spectral measures and dynamics $h [electronic resource] : $b typical behaviors / $c by Moacir Aloisio, Silas L. Carvalho, César R. de Oliveira.
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505 0 $a Spectrum and Dynamics: Some Basic Concepts -- Part I Quantum Models: Correlation Dimension -- Fractal Measures and Dynamics -- Escaping Probabilities and Quasiballistic Dynamics -- Generalized Dimensions and Dynamics -- Part II Ergodic Theory and Semigroups: Generic Scales of Weak-Mixing -- Asymptotics of C0-Semigroups -- Generic Stability for Self-adjoint Semigroups -- References.
520 $a 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.
650 0 $a Spectral theory (Mathematics) $3 182365
650 0 $a Linear operators. $3 286712
650 1 4 $a Mathematical Physics. $3 522725
650 2 4 $a Measure and Integration. $3 273777
650 2 4 $a Quantum Physics. $3 275010
650 2 4 $a Differential Equations. $3 285983
700 1 $a Carvalho, Silas L. $3 962716
700 1 $a de Oliveira, Cesar R. $3 962717
710 2 $a SpringerLink (Online service) $3 273601
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856 4 0 $u https://doi.org/10.1007/978-3-031-38289-5
950 $a Mathematics and Statistics (SpringerNature-11649)