Functional Analysis (Graduate Studies in Mathematics, 191, Band 191) - Hardcover

Buch 152�von 190: Graduate Studies in Mathematics

Buhler, Theo ; Salamon, Dietmar A.

9781470441906: Functional Analysis (Graduate Studies in Mathematics, 191, Band 191)

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ISBN 10: 147044190X ISBN 13: 9781470441906

Verlag: American Mathematical Society, 2018

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This textbook is for a first course in functional analysis for students who have completed first-year courses in analysis and linear algebra and second-year courses in complex analysis, topology, and measure and integration. B�hler and Salamon assume that students have studied elementary Hilbert space theory, the Stone-Weierstra� Theorem, and the lemma of Zorn and Tychonoff's Theorem in previous courses, but include them here for completeness. They cover foundations, principles of functional analysis, the weak and weak* topologies, Fredhold theory, spectral theory, unbounded operators, and semigroups of operators. Annotation �2018 Ringgold, Inc., Portland, OR (protoview.com)

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Verlag: American Mathematical Society
Erscheinungsdatum: 2018
Sprache: Englisch
ISBN 10: 147044190X
ISBN 13: 9781470441906
Einband: Gebundene Ausgabe
Anzahl der Seiten: 466
Kontakt zum Hersteller: Nicht verf�gbar
Verantwortliche Person: Buchb�r
info@buchbaer.de

Weberstr. 67
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Functional Analysis

Buhler, Theo, Salamon, Dietmar A.

Verlag: American Mathematical Society, 2018

ISBN 10: 147044190X ISBN 13: 9781470441906

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Functional Analysis (eng)

Theo Buhler

Verlag: American Mathematical Society, 2018

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Functional Analysis

Theo Buhler

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Buhler, Theo; Salamon, Dietmar A.

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Buhler, Theo/ Salamon, Dietmar A.

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Functional Analysis

Theo Buhler, Dietmar A. Salamon

Verlag: American Mathematical Society, US, 2018

ISBN 10: 147044190X ISBN 13: 9781470441906

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Hardback. Zustand: New. Functional analysis is a central subject of mathematics with applications in many areas of geometry, analysis, and physics. This book provides a comprehensive introduction to the field for graduate students and researchers. It begins in Chapter 1 with an introduction to the necessary foundations, including the Arzela-Ascoli theorem, elementary Hilbert space theory, and the Baire Category Theorem. Chapter 2 develops the three fundamental principles of functional analysis (uniform boundedness, open mapping theorem, Hahn-Banach theorem) and discusses reflexive spaces and the James space. Chapter 3 introduces the weak and weak$^*$ topologies and includes the theorems of Banach-Alaoglu, Banach-Dieudonne, Eberlein-Smulyan, Krein-Milman, as well as an introduction to topological vector spaces and applications to ergodic theory. Chapter 4 is devoted to Fredholm theory. It includes an introduction to the dual operator and to compact operators, and it establishes the closed image theorem. Chapter 5 deals with the spectral theory of bounded linear operators. It introduces complex Banach and Hilbert spaces, the continuous functional calculus for self-adjoint and normal operators, the Gelfand spectrum, spectral measures, cyclic vectors, and the spectral theorem. Chapter 6 introduces unbounded operators and their duals. It establishes the closed image theorem in this setting and extends the functional calculus and spectral measure to unbounded self-adjoint operators on Hilbert spaces. Chapter 7 gives an introduction to strongly continuous semigroups and their infinitesimal generators. It includes foundational results about the dual semigroup and analytic semigroups, an exposition of measurable functions with values in a Banach space, and a discussion of solutions to the inhomogeneous equation and their regularity properties. The appendix establishes the equivalence of the Lemma of Zorn and the Axiom of Choice, and it contains a proof of Tychonoff's theorem. With 10 to 20 elaborate exercises at the end of each chapter, this book can be used as a text for a one-or-two-semester course on functional analysis for beginning graduate students. Prerequisites are first-year analysis and linear algebra, as well as some foundational material from the second-year courses on point set topology, complex analysis in one variable, and measure and integration. Bestandsnummer des Verk�ufers LU-9781470441906

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