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Bücher Wissen & Bildung Geisteswissenschaft, Kunst, Musik Geisteswissenschaft allg. Real and Functional Analysis
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Real and Functional Analysis
Serge Lang (Gebundene Ausgabe, Deutsch)
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Beschreibung
This 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. Dieses Produkt haben wir gerade leider nicht auf Lager.
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Technische Daten
Erscheinungsdatum
01.01.1996
Sprache
Deutsch
EAN
9783540940012
Herausgeber
Springer Berlin
Serien- oder Bandtitel
Graduate Texts in Mathematics
Sonderedition
Nein
Autor
Serge Lang
Seitenanzahl
580
Einbandart
Gebundene Ausgabe
Bandzählung
142
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