A Course in Functional Analysis and Measure Theory

Written by an expert on the topic and experienced lecturer, this textbook provides an elegant, self-contained introduction to functional analysis, including several advanced topics and applications to harmonic analysis. Starting from basic topics before proceeding to more advanced material, the book...

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Hlavní autor: Kadets, Vladimir (Autor)
Médium: Elektronický zdroj E-kniha
Jazyk:angličtina
Vydáno: Cham : Springer International Publishing, 2018.
Vydání:1st ed. 2018.
Edice:Universitext,
Témata:
Functional analysis.
Measure theory.
Operator theory.
Functions of real variables.
ISBN:9783319920047
ISSN:0172-5939
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Obsah:
  • Introduction
  • Chapter 1. Metric and topological spaces
  • Chapter 2. Measure theory
  • Chapter 3. Measurable functions
  • Chapter 4. The Lebesgue integral
  • Chapter 5. Linear spaces, linear functionals, and the Hahn-Banach theorem
  • Chapter 6. Normed spaces
  • Chapter 7. Absolute continuity of measures and functions. Connection between derivative and integral
  • Chapter 8. The integral on C(K)
  • Chapter 9. Continuous linear functionals
  • Chapter 10. Classical theorems on continuous operators
  • Chapter 11. Elements of spectral theory of operators. Compact operators
  • Chapter 12. Hilbert spaces
  • Chapter 13. Functions of an operator
  • Chapter 14. Operators in Lp
  • Chapter 15. Fixed-point theorems and applications
  • Chapter 16. Topological vector spaces
  • Chapter 17. Elements of duality theory
  • Chapter 18. The Krein-Milman theorem and applications
  • References. Index.

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