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Linear functional analysis : an application-oriented introduction / Hans Wilhelm Alt and translated by Robert Nurnberg.

By: Contributor(s): Material type: TextTextSeries: UniversitextPublication details: London : Springer-Verlag, 2016.Description: xii, 435 pages : illustrations ; 24 cmISBN:
  • 9781447172796
Subject(s): DDC classification:
  • 515.7 23 Al465
Contents:
1. Introduction.- 2. Preliminaries.- 3. Function spaces.- 4. Subsets of function spaces.- 5. Linear operators.- 6. Linear functionals.- 7. Uniform boundedness principle.- 8. Weak convergence.- 9. Finite-dimensional approximation.- 10. Compact operators.- 11. Spectrum of compact operators.- 12. Self-adjoint operators.- References.- Symbols.- Index.
Summary: This book gives an introduction to Linear Functional Analysis, which is a synthesis of algebra, topology, and analysis. In addition to the basic theory it explains operator theory, distributions, Sobolev spaces, and many other things. The text is self-contained and includes all proofs, as well as many exercises, most of them with solutions. Moreover, there are a number of appendices, for example on Lebesgue integration theory.
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Includes bibliographical references and index.

1. Introduction.-
2. Preliminaries.-
3. Function spaces.-
4. Subsets of function spaces.-
5. Linear operators.-
6. Linear functionals.-
7. Uniform boundedness principle.-
8. Weak convergence.-
9. Finite-dimensional approximation.-
10. Compact operators.-
11. Spectrum of compact operators.-
12. Self-adjoint operators.-
References.-
Symbols.-
Index.

This book gives an introduction to Linear Functional Analysis, which is a synthesis of algebra, topology, and analysis. In addition to the basic theory it explains operator theory, distributions, Sobolev spaces, and many other things. The text is self-contained and includes all proofs, as well as many exercises, most of them with solutions. Moreover, there are a number of appendices, for example on Lebesgue integration theory.

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