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100   $a20171121d2017      u|         0
101 0 $aeng
135   $aurnn#008mamaa
181   $ctxt$2rdacontent
182   $cc$2rdamedia
183   $acr$2rdacarrier
200 10$aFunctional Analysis, Spectral Theory, and Applications /$fby Manfred Einsiedler, Thomas Ward
205   $a1st ed. 2017.
210  1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2017.
215   $a1 online resource (XIV, 614 p. 33 illus.)
225 1 $aGraduate Texts in Mathematics,$x2197-5612 ;$v276
311 08$a3-319-58539-8 
327   $aMotivation -- Norms and Banach Spaces -- Hilbert Spaces, Fourier Series, Unitary Representations -- Uniform Boundedness and Open Mapping Theorem -- Sobolev Spaces and Dirichlet?s Boundary Problem -- Compact Self-Adjoint Operators, Laplace Eigenfunctions -- Dual Spaces -- Locally Convex Vector Spaces -- Unitary Operators and Flows, Fourier Transform -- Locally Compact Groups, Amenability, Property (T) -- Banach Algebras and the Spectrum -- Spectral Theory and Functional Calculus -- Self-Adjoint and Symmetric Operators -- The Prime Number Theorem -- Appendix A: Set Theory and Topology -- Appendix B: Measure Theory -- Hints for Selected Problems -- Notes. .
330   $aThis textbook provides a careful treatment of functional analysis and some of its applications in analysis, number theory, and ergodic theory. In addition to discussing core material in functional analysis, the authors cover more recent and advanced topics, including Weyl?s law for eigenfunctions of the Laplace operator, amenability and property (T), the measurable functional calculus, spectral theory for unbounded operators, and an account of Tao?s approach to the prime number theorem using Banach algebras. The book further contains numerous examples and exercises, making it suitable for both lecture courses and self-study. Functional Analysis, Spectral Theory, and Applications is aimed at postgraduate and advanced undergraduate students with some background in analysis and algebra, but will also appeal to everyone with an interest in seeing how functional analysis can be applied to other parts of mathematics.
410  0$aGraduate Texts in Mathematics,$x2197-5612 ;$v276
606   $aFunctional analysis
606   $aDifferential equations
606   $aHarmonic analysis
606   $aNumber theory
606   $aDynamics
606   $aFunctional Analysis
606   $aDifferential Equations
606   $aAbstract Harmonic Analysis
606   $aNumber Theory
606   $aDynamical Systems
615  0$aFunctional analysis.
615  0$aDifferential equations.
615  0$aHarmonic analysis.
615  0$aNumber theory.
615  0$aDynamics.
615 14$aFunctional Analysis.
615 24$aDifferential Equations.
615 24$aAbstract Harmonic Analysis.
615 24$aNumber Theory.
615 24$aDynamical Systems.
676   $a515.7
686   $a46$2MSC
700   $aEinsiedler$b Manfred$4aut$4http://id.loc.gov/vocabulary/relators/aut$0477516
702   $aWard$b Thomas$4aut$4http://id.loc.gov/vocabulary/relators/aut
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
906   $aBOOK
912   $a9910254293003321
996   $aFunctional Analysis, Spectral Theory, and Applications$92296097
997   $aUNINA