001482757 000__ 04539cam\\22005897i\4500
001482757 001__ 1482757
001482757 003__ OCoLC
001482757 005__ 20231128003350.0
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001482757 008__ 231101s2023\\\\sz\a\\\\ob\\\\001\0\eng\d
001482757 019__ $$a1406806630$$a1406828267
001482757 020__ $$a9783031382895$$q(electronic bk.)
001482757 020__ $$a3031382897$$q(electronic bk.)
001482757 020__ $$z9783031382888
001482757 020__ $$z3031382889
001482757 0247_ $$a10.1007/978-3-031-38289-5$$2doi
001482757 035__ $$aSP(OCoLC)1407066202
001482757 040__ $$aGW5XE$$beng$$erda$$epn$$cGW5XE$$dYDX$$dOCLKB$$dYDX$$dOCLCO
001482757 049__ $$aISEA
001482757 050_4 $$aQA320$$b.A46 2023
001482757 08204 $$a515/.7222$$223/eng/20231101
001482757 1001_ $$aAloisio, Moacir,$$eauthor.$$0(orcid)0000-0001-7749-5206$$1https://orcid.org/0000-0001-7749-5206
001482757 24510 $$aSpectral measures and dynamics :$$btypical behaviors /$$cMoacir Aloisio, Silas L. Carvalho, César R. de Oliveira.
001482757 264_1 $$aCham :$$bSpringer,$$c2023.
001482757 300__ $$a1 online resource (xi, 246 pages) :$$bcolor illustrations.
001482757 336__ $$atext$$btxt$$2rdacontent
001482757 337__ $$acomputer$$bc$$2rdamedia
001482757 338__ $$aonline resource$$bcr$$2rdacarrier
001482757 4901_ $$aLatin American Mathematics Series -- UFSCar subseries,$$x2524-6763
001482757 504__ $$aIncludes bibliographical references and index.
001482757 5050_ $$aSpectrum 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.
001482757 506__ $$aAccess limited to authorized users.
001482757 520__ $$aThis 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.
001482757 588__ $$aOnline resource; title from PDF title page (SpringerLink, viewed October 30, 2023).
001482757 650_6 $$aSpectre (Mathématiques)
001482757 650_6 $$aOpérateurs linéaires.
001482757 650_0 $$aSpectral theory (Mathematics)$$0(DLC)sh 85126408
001482757 650_0 $$aLinear operators.
001482757 655_0 $$aElectronic books.
001482757 7001_ $$aCarvalho, Silas L.$$eauthor.$$0(orcid)0000-0003-2493-0627$$1https://orcid.org/0000-0003-2493-0627
001482757 7001_ $$ade Oliveira, César R.$$eauthor.$$0(orcid)0000-0002-1926-8934$$1https://orcid.org/0000-0002-1926-8934
001482757 77608 $$iPrint version: $$z3031382889$$z9783031382888$$w(OCoLC)1382625401
001482757 830_0 $$aLatin American Mathematics Series.$$pUFSCar subseries,$$x2524-6763
001482757 852__ $$bebk
001482757 85640 $$3Springer Nature$$uhttps://univsouthin.idm.oclc.org/login?url=https://link.springer.com/10.1007/978-3-031-38289-5$$zOnline Access$$91397441.1
001482757 909CO $$ooai:library.usi.edu:1482757$$pGLOBAL_SET
001482757 980__ $$aBIB
001482757 980__ $$aEBOOK
001482757 982__ $$aEbook
001482757 983__ $$aOnline
001482757 994__ $$a92$$bISE