LEADER 04466nam 22006375 450 001 996466396203316 005 20240207101418.0 010 $a3-030-67462-2 024 7 $a10.1007/978-3-030-67462-5 035 $a(CKB)4100000011918695 035 $a(DE-He213)978-3-030-67462-5 035 $a(MiAaPQ)EBC6607269 035 $a(Au-PeEL)EBL6607269 035 $a(OCoLC)1256241674 035 $a(PPN)255882092 035 $a(EXLCZ)994100000011918695 100 $a20210506d2021 u| 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 12$aA Guide to Spectral Theory$b[electronic resource] $eApplications and Exercises /$fby Christophe Cheverry, Nicolas Raymond 205 $a1st ed. 2021. 210 1$aCham :$cSpringer International Publishing :$cImprint: Birkhäuser,$d2021. 215 $a1 online resource (XX, 258 p. 2 illus.) 225 1 $aBirkhäuser Advanced Texts Basler Lehrbücher,$x2296-4894 311 $a3-030-67461-4 327 $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?s 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 -- Bibliography -- Index. 330 $aThis textbook provides a graduate-level introduction to the spectral theory of linear operators on Banach and Hilbert spaces, guiding readers through key components of spectral theory and its applications in quantum physics. Based on their extensive teaching experience, the authors present topics in a progressive manner so that each chapter builds on the ones preceding. Researchers and students alike will also appreciate the exploration of more advanced applications and research perspectives presented near the end of the book. Beginning with a brief introduction to the relationship between spectral theory and quantum physics, the authors go on to explore unbounded operators, analyzing closed, adjoint, and self-adjoint operators. Next, the spectrum of a closed operator is defined and the fundamental properties of Fredholm operators are introduced. The authors then develop the Grushin method to execute the spectral analysis of compact operators. The chapters that follow are devoted to examining Hille-Yoshida and Stone theorems, the spectral analysis of self-adjoint operators, and trace-class and Hilbert-Schmidt operators. The final chapter opens the discussion to several selected applications. Throughout this textbook, detailed proofs are given, and the statements are illustrated by a number of well-chosen examples. At the end, an appendix about foundational functional analysis theorems is provided to help the uninitiated reader. A Guide to Spectral Theory: Applications and Exercises is intended for graduate students taking an introductory course in spectral theory or operator theory. A background in linear functional analysis and partial differential equations is assumed; basic knowledge of bounded linear operators is useful but not required. PhD students and researchers will also find this volume to be of interest, particularly the research directions provided in later chapters. 410 0$aBirkhäuser Advanced Texts Basler Lehrbücher,$x2296-4894 606 $aFunctional analysis 606 $aDifferential equations 606 $aMathematical physics 606 $aFunctional Analysis 606 $aDifferential Equations 606 $aMathematical Physics 606 $aTeoria espectral (Matemàtica)$2thub 608 $aLlibres electrònics$2thub 615 0$aFunctional analysis. 615 0$aDifferential equations. 615 0$aMathematical physics. 615 14$aFunctional Analysis. 615 24$aDifferential Equations. 615 24$aMathematical Physics. 615 7$aTeoria espectral (Matemàtica) 676 $a515.7222 700 $aCheverry$b Christophe$0977155 702 $aRaymond$b Nicolas 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996466396203316 996 $aA Guide to Spectral Theory$92226065 997 $aUNISA