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This title in other editionsOther titles in the Pure and Applied Mathematics: A WileyInterscience Series of Texts, Monographs and Tracts series:
Functional Analysis (Pure and Applied Mathematics: A WileyInterscience Series of Texts, Monographs and Tracts)by Peter D. Lax
Synopses & ReviewsPublisher Comments:Includes sections on the spectral resolution and spectral representation of self adjoint operators, invariant subspaces, strongly continuous oneparameter semigroups, the index of operators, the trace formula of Lidskii, the Fredholm determinant, and more.
* Assumes prior knowledge of Naive set theory, linear algebra, point set topology, basic complex variable, and real variables. * Includes an appendix on the Riesz representation theorem. Book News Annotation:Designed for a twosemester course at the graduate level, this text describes the theory and applications of functional analysis. In 38 short chapters, Lax (emeritus, mathematics, New York U.) addresses such topics as Banach spaces, weak sequential topologies, the Krein Milman theorem, the Fredholm determinant, and scattering theory. Included in the appendices are a functional analytic proof of the RieszKakutani representation theorem and an outline of the theory of distributions.
Annotation c. Book News, Inc., Portland, OR (booknews.com) Synopsis:Offers graduate level coverage of functional analysis, including standard topics such as topology, linear operators, and Gelfand's theory of commutative Banach algebras. Problems and exercises are included.
Synopsis:* Includes an appendix on the Riesz representation theorem.
Synopsis:Funktionalanalysis für Fortgeschrittene: Hier erfahren Sie alles über Topologie, lineare Operatoren, die Gelfandsche Theorie kommutativer BanachAlgebren und vieles andere. Mit durchgerechneten Beispielen und Übungsaufgaben!
Table of ContentsForeword.
Linear Spaces. Linear Maps. The HahnBanach Theorem. Applications of the HahnBanach Theorem. Normed Linear Spaces. Hilbert Space. Applications of Hilbert Space Results. Duals of Normed Linear Space. Applications of Duality. Weak Convergence. Applications of Weak Convergence. The Weak and Weak* Topologies. Locally Convex Topologies and the KreinMilman Theorem. Examples of Convex Sets and their Extreme Points. Bounded Linear Maps. Examples of Bounded Linear Maps. Banach Algebras and their Elementary Spectral Theory. Gelfand's Theory of Commutative Banach Algebras. Applications of Gelfand's Theory of Commutative Banach Algebras. Examples of Operators and their Spectra. Compact Maps. Examples of Compact Operators. Positive Compact Operators. Fredholm's Theory of Integral Equations. Invariant Subspaces. Harmonic Analysis on a Halfline. Index Theory. Compact Symmetric Operators in Hilbert Space. Examples of Compact Symmetric Operators. Trace Class and Trace Formula. Spectral Theory of Symmetric, Normal and Unitary Operators. Spectral Theory of SelfAdjoint Operators. Examples of SelfAdjoint Operators. Semigroups of Operators. Groups of Unitary Operators. Examples of Strongly Continuous Semigroups. Scattering Theory. A Theorem of Beurling. Appendix A: The RieszKakutani Representation Theorem. Appendix B: Theory of Distributions. Appendix C: Zorn's Lemma. Author Index. Subject Index. What Our Readers Are SayingBe the first to add a comment for a chance to win!Product Details
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