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_b eng
_c WSPC
020 _a9789811215506
_q(ebook)
020 _a9811215502
_q(ebook)
020 _z9811215499
_q(hbk.)
020 _z9789811215490
_q(hbk.)
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_q(pbk.)
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_q(pbk.)
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_b.J27 2020
072 7 _aMAT
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_2bisacsh
082 0 4 _a515
_223
100 1 _aJacob, Niels.
_920859
245 1 0 _aCourse in analysis.
_nVol 5.
_pFunctional analysis, some operator theory & theory of distributions
_h[electronic resource] /
_cNiels Jacob, Kristian P. Evans.
246 3 0 _aFunctional analysis, some operator theory & theory of distributions
260 _aSingapore :
_bWorld Scientific,
_c2020.
300 _a1 online resource (856 p.)
504 _aIncludes bibliographical references and index.
505 0 _aFunctional 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.
520 _a"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.
538 _aMode of access: World Wide Web.
538 _aSystem requirements: Adobe Acrobat reader.
650 0 _aMathematical analysis
_vTextbooks.
_912177
650 0 _aMathematics
_xStudy and teaching (Higher)
_920860
650 0 _aCalculus
_vTextbooks.
_921240
655 0 _aElectronic books.
_93294
700 1 _aEvans, Kristian P.
_920863
856 4 0 _uhttps://www.worldscientific.com/worldscibooks/10.1142/11695#t=toc
_zAccess to full text is restricted to subscribers.
942 _cEBK
999 _c72791
_d72791