Functional analysis /

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Detalles Bibliográficos
Autor principal: Lax, Peter D.
Formato: Libro
Lenguaje:English
Publicado: New York : Wiley-Interscience, c2002.
Colección:Pure and applied mathematics
Materias:
Análisis funcional.
Tabla de Contenidos:
  • 1. Linear spaces
  • 2. Linear maps
  • 3. The Hahn-Banach theorem
  • 4. Applications of the Hahn-Banach theorem
  • 5. Normed linear spaces
  • 6. Hilbert space
  • 7. Applications of Hilbert space results
  • 8. Duals of normed linear spaces
  • 9. Applications of duality
  • 10. Weak convergence
  • 11. Applications of weak convergence
  • 12. The weak and weak topologies
  • 13. Locally convex topologies and the Krein-Milman theorem
  • 14. Examples of convex sets and their extreme points
  • 15. Bounded linear maps
  • 16. Examples of bounded linear maps
  • 17. Banach algebras and their elementary spectral theory
  • 18. Gelfand's theory of commutative Banach algebras
  • 19. Applications of Gelfand's theory of commutative Banach algebras
  • 20. Examples of operators and their spectra
  • 21. Compact maps
  • 22. Examples of compact operators
  • 23. Positive compact operators
  • 24. Fredholm's theory of integral equations
  • 25. Invariant subspaces
  • 26. Harmonic analysis on a halfline
  • 27. Index theory
  • 28. Compact symmetric operators in Hilbert space
  • 29. Examples of compact symmetric operators
  • 30. Trace class and trace formula
  • 31. Spectral theory of symmetric, normal, and unitary operators
  • 32. Spectral theory of self-adjoint operators
  • 33. Examples of self-adjoint operators
  • 34. Semigroups of operators
  • 35. Groups of unitary operators
  • 36. Examples of strongly continuous semigroups
  • 37. Scattering theory
  • 38. A theorem of Beurling.

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