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Title
Real and Functional Analysis / by Serge Lang.
Edition
Third edition.
ISBN
9781461208976 (electronic book)
1461208971 (electronic book)
9781461269380
1461269385
1461208971
Publication Details
New York, NY : Springer New York, 1993.
Language
English
Language Note
English.
Description
1 online resource (xiv, 580 pages)
Item Number
10.1007/978-1-4612-0897-6 doi
Call Number
QA331.5
Dewey Decimal Classification
515.8
Summary
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.
Access Note
Access limited to authorized users.
Digital File Characteristics
text file PDF
Series
Graduate texts in mathematics ; 142.
Available in Other Form
Print version: 9781461269380
I 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.
