Includes bibliographical references and index.

Functional analysis: What is functional analysis about? -- Infinite dimensional vector spaces -- Banach spaces -- Linear operators and linear functionals -- The dual space -- The basic principles of functional analysis -- Adjoint operators and Fredholm theory -- Hilbert spaces and operators in Hilbert spaces -- Unbounded operators in Hilbert spaces -- Spectral theory. Part I: Gelfand-Naimark theory -- Spectral theory. Part II: Self-adjoint operators -- Topological vector spaces -- convexity and integral representations -- Selected topics - Some operator theory: some integral operators -- One-parameter semigroups of operators -- Positivity preserving operators and Markovian semigroups -- On regular Sturm-Liouville problems -- Sobolev spaces. A first encounter -- Operators induced by the Dirichlet problem -- Selected topics - Distributions. Some function spaces as Fréchet spaces -- Distributions in the sense of Schwartz -- Further properties of distributions -- Tempered distributions and the Fourier transform -- Tensor products and the kernel theorem -- Calderon-Zygmund operators - Appendices: Completeness --nets, convergence and continuity -- On the Riesz representation theorem -- Solutions to problems of Part 12 -- Solutions to problems of Part 13 -- Solutions to problems of Part 14 - References -- Mathematicians contributing to analysis (continued) -- Subject index.

"The book is an advanced textbook and a reference text in functional analysis in the wide sense. It provides advanced undergraduate and graduate students with a coherent introduction to the field, i.e. the basic principles, and leads them to more demanding topics such as the spectral theorem, Choquet theory, interpolation theory, analysis of operator semigroups, Hilbert-Schmidt operators and Hille-Tamarkin operators, topological vector spaces and distribution theory, fundamental solutions, or the Schwartz kernel theorem. All topics are treated in great detail and the text provided is suitable for self-studying the subject. This is enhanced by more than 270 problems solved in detail. At the same time the book is a reference text for any working mathematician needing results from functional analysis, operator theory or the theory of distributions. Embedded as Volume V in the Course of Analysis, readers will have a self-contained treatment of a key area in modern mathematics. A detailed list of references invites to further studies"--Publisher's website.

Mode of access: World Wide Web.

System requirements: Adobe Acrobat reader.