Real and Functional Analysis: v. 142 - Rilegato

Lang, Serge

Rilegato

ISBN 10: 3540940014 ISBN 13: 9783540940012

Casa editrice: Springer-Verlag Berlin and Heidelberg GmbH & Co. K, 1993

Riassunto

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 it is 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 4 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.

Su questa edizione

• Editore: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
• Data di pubblicazione: 1993
• ISBN 10: 3540940014
• ISBN 13: 9783540940012
• Rilegatura: Copertina rigida
• Numero edizione: 3
• Numero di pagine: 394