000 04183nam a22006015i 4500
001 978-3-319-58540-6
003 DE-He213
005 20181204134423.0
007 cr nn 008mamaa
008 171121s2017 gw | s |||| 0|eng d
020 _a9783319585406
_9978-3-319-58540-6
024 7 _a10.1007/978-3-319-58540-6
_2doi
040 _aISI Library, Kolkata
050 4 _aQA319-329.9
072 7 _aPBKF
_2bicssc
072 7 _aMAT037000
_2bisacsh
072 7 _aPBKF
_2thema
082 0 4 _a515.7
_223
100 1 _aEinsiedler, Manfred.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 0 _aFunctional Analysis, Spectral Theory, and Applications
_h[electronic resource] /
_cby Manfred Einsiedler, Thomas Ward.
264 1 _aCham :
_bSpringer International Publishing :
_bImprint: Springer,
_c2017.
300 _aXIV, 614 p. 33 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aGraduate Texts in Mathematics,
_x0072-5285 ;
_v276
505 0 _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.
520 _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.
650 0 _aFunctional analysis.
650 0 _aDifferential Equations.
650 0 _aDifferential equations, partial.
650 0 _aHarmonic analysis.
650 0 _aNumber theory.
650 0 _aDifferentiable dynamical systems.
650 1 4 _aFunctional Analysis.
_0http://scigraph.springernature.com/things/product-market-codes/M12066
650 2 4 _aOrdinary Differential Equations.
_0http://scigraph.springernature.com/things/product-market-codes/M12147
650 2 4 _aPartial Differential Equations.
_0http://scigraph.springernature.com/things/product-market-codes/M12155
650 2 4 _aAbstract Harmonic Analysis.
_0http://scigraph.springernature.com/things/product-market-codes/M12015
650 2 4 _aNumber Theory.
_0http://scigraph.springernature.com/things/product-market-codes/M25001
650 2 4 _aDynamical Systems and Ergodic Theory.
_0http://scigraph.springernature.com/things/product-market-codes/M1204X
700 1 _aWard, Thomas.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783319585390
776 0 8 _iPrinted edition:
_z9783319585413
776 0 8 _iPrinted edition:
_z9783319864235
830 0 _aGraduate Texts in Mathematics,
_x0072-5285 ;
_v276
856 4 0 _uhttps://doi.org/10.1007/978-3-319-58540-6
912 _aZDB-2-SMA
942 _cEB
950 _aMathematics and Statistics (Springer-11649)
999 _c427370
_d427370