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000928533 019__ $$a1112952983
000928533 020__ $$a9781461208976$$q(electronic book)
000928533 020__ $$a1461208971$$q(electronic book)
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000928533 0247_ $$a10.1007/978-1-4612-0897-6$$2doi
000928533 035__ $$aSP(OCoLC)ocn853268708
000928533 035__ $$aSP(OCoLC)853268708$$z(OCoLC)1112952983
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000928533 049__ $$aISEA
000928533 050_4 $$aQA331.5
000928533 08204 $$a515.8$$223
000928533 1001_ $$aLang, Serge.
000928533 24510 $$aReal and Functional Analysis /$$cby Serge Lang.
000928533 250__ $$aThird edition.
000928533 260__ $$aNew York, NY :$$bSpringer New York,$$c1993.
000928533 300__ $$a1 online resource (xiv, 580 pages)
000928533 336__ $$atext$$btxt$$2rdacontent
000928533 337__ $$acomputer$$bc$$2rdamedia
000928533 338__ $$aonline resource$$bcr$$2rdacarrier
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000928533 4901_ $$aGraduate Texts in Mathematics,$$x0072-5285 ;$$v142
000928533 5050_ $$aI Sets -- II Topological Spaces -- III Continuous Functions on Compact Sets -- IV Banach Spaces -- V Hilbert Space -- VI The General Integral -- VII Duality and Representation Theorems -- VIII Some Applications of Integration -- IX Integration and Measures on Locally Compact Spaces -- X Riemann-Stieltjes Integral and Measure -- XI Distributions -- XII Integration on Locally Compact Groups -- XIII Differential Calculus -- XIV Inverse Mappings and Differential Equations -- XV The Open Mapping Theorem, Factor Spaces, and Duality -- XVI The Spectrum -- XVII Compact and Fredholm Operators -- XVIII Spectral Theorem for Bounded Hermltian Operators -- XIX Further Spectral Theorems -- XX Spectral Measures -- XXI Local Integration off Differential Forms -- XXII Manifolds -- XXIII Integration and Measures on Manifolds -- Table of Notation.
000928533 506__ $$aAccess limited to authorized users.
000928533 520__ $$aThis book is meant as a text for a first-year graduate course in analysis. In a sense, the subject matter covers the same topics as elementary calculus - linear algebra, differentiation, integration - but treated in a manner suitable for people who will be using it in further mathematical investigations. The book begins with point-set topology, essential for all analysis. The second part deals with the two basic spaces of analysis, Banach and Hilbert spaces. The book then turns to the subject of integration and measure. After a general introduction, it covers duality and representation theorems, some applications (such as Dirac sequences and Fourier transforms), integration and measures on locally compact spaces, the Riemann-Stjeltes integral, distributions, and integration on locally compact groups. Part four deals with differential calculus (with values in a Banach space). The next part deals with functional analysis. It includes several major spectral theorems of analysis, showing how one can extend to infinite dimensions certain results from finite-dimensional linear algebra; a discussion of compact and Fredholm operators; and spectral theorems for Hermitian operators. The final part, on global analysis, provides an introduction to differentiable manifolds. The text includes worked examples and numerous exercises, which should be viewed as an integral part of the book. The organization of the book avoids long chains of logical interdependence, so that chapters are as independent as possible. This allows a course using the book to omit material from some chapters without compromising the exposition of material from later chapters.
000928533 546__ $$aEnglish.
000928533 650_0 $$aMathematics.
000928533 77608 $$iPrint version:$$z9781461269380
000928533 830_0 $$aGraduate texts in mathematics ;$$v142.
000928533 852__ $$bebk
000928533 85640 $$3SpringerLink$$uhttps://univsouthin.idm.oclc.org/login?url=http://link.springer.com/10.1007/978-3-030-38219-3$$zOnline Access$$91397441.1
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000928533 980__ $$aEBOOK
000928533 980__ $$aBIB
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000928533 983__ $$aOnline
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