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001436473 001__ 1436473
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001436473 019__ $$a1250347906$$a1251449185$$a1253556769$$a1255224704$$a1255233034
001436473 020__ $$a9783030674625$$q(electronic bk.)
001436473 020__ $$a3030674622$$q(electronic bk.)
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001436473 020__ $$z9783030674618$$q(print)
001436473 0247_ $$a10.1007/978-3-030-67462-5$$2doi
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001436473 049__ $$aISEA
001436473 050_4 $$aQA320
001436473 08204 $$a515/.7222$$223
001436473 1001_ $$aCheverry, Christophe.
001436473 24512 $$aA guide to spectral theory :$$bapplications and exercises /$$cChristophe Cheverry, Nicolas Raymond.
001436473 260__ $$aCham :$$bBirkhäuser,$$c2021.
001436473 300__ $$a1 online resource (xx, 258 pages)
001436473 336__ $$atext$$btxt$$2rdacontent
001436473 337__ $$acomputer$$bc$$2rdamedia
001436473 338__ $$aonline resource$$bcr$$2rdacarrier
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001436473 347__ $$bPDF
001436473 4901_ $$aBirkhäuser advanced texts Basler Lehrbücher,$$x1019-6242
001436473 504__ $$aIncludes bibliographical references and index.
001436473 5050_ $$aForeword -- Prolegomena -- Chapter 1: A First Look at Spectral Theory -- Chapter 2: Unbounded Operators -- Chapter 3: Spectrum -- Chapter 4: Compact Operators -- Chapter 5: Fredholm Theory -- Chapter 6:Spectrum of Self-Adjoint Operators -- Chapter 7: Hille-Yosida and Stone Theorems -- Chapter 8: About the Spectral Measure -- Chapter 9: Trace-class and Hilbert-Schmidt Operators -- Chapter 10: Selected Applications of the Functional Calculus -- Appendix A: Reminders of Functional Analysis.
001436473 506__ $$aAccess limited to authorized users.
001436473 520__ $$aThis textbook provides a graduate-level introduction to the spectral theory of linear operators on Banach and Hilbert spaces, guiding readers through key components of spectral theory and its applications in quantum physics. Based on their extensive teaching experience, the authors present topics in a progressive manner so that each chapter builds on the ones preceding. Researchers and students alike will also appreciate the exploration of more advanced applications and research perspectives presented near the end of the book. Beginning with a brief introduction to the relationship between spectral theory and quantum physics, the authors go on to explore unbounded operators, analyzing closed, adjoint, and self-adjoint operators. Next, the spectrum of a closed operator is defined and the fundamental properties of Fredholm operators are introduced. The authors then develop the Grushin method to execute the spectral analysis of compact operators. The chapters that follow are devoted to examining Hille-Yoshida and Stone theorems, the spectral analysis of self-adjoint operators, and trace-class and Hilbert-Schmidt operators. The final chapter opens the discussion to several selected applications. Throughout this textbook, detailed proofs are given, and the statements are illustrated by a number of well-chosen examples. At the end, an appendix about foundational functional analysis theorems is provided to help the uninitiated reader. A Guide to Spectral Theory: Applications and Exercises is intended for graduate students taking an introductory course in spectral theory or operator theory. A background in linear functional analysis and partial differential equations is assumed; basic knowledge of bounded linear operators is useful but not required. PhD students and researchers will also find this volume to be of interest, particularly the research directions provided in later chapters.
001436473 588__ $$aOnline resource; title from PDF title page (SpringerLink, viewed May 11, 2021).
001436473 650_0 $$aSpectral theory (Mathematics)
001436473 650_0 $$aLinear operators.
001436473 650_6 $$aSpectre (Mathématiques)
001436473 650_6 $$aOpérateurs linéaires.
001436473 655_7 $$aTextbooks.$$2fast$$0(OCoLC)fst01423863
001436473 655_7 $$aTextbooks.$$2lcgft
001436473 655_0 $$aElectronic books.
001436473 7001_ $$aRaymond, Nicolas,$$eauthor.
001436473 77608 $$iPrint version: $$z3030674614$$z9783030674618$$w(OCoLC)1226764100
001436473 830_0 $$aBirkhäuser advanced texts,$$x1019-6242
001436473 852__ $$bebk
001436473 85640 $$3Springer Nature$$uhttps://univsouthin.idm.oclc.org/login?url=https://link.springer.com/10.1007/978-3-030-67462-5$$zOnline Access$$91397441.1
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