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Spectral Measures and Dynamics: Typical Behaviors
Hardcover
ISBN13: 9783031382888
Publisher: Springer
Published: Oct 28 2023
Pages: 246
Weight: 1.19
Height: 0.63 Width: 6.14 Depth: 9.21
Language: English
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 singularcontinuous 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.
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