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    Gebundenes Buch

Funktionalanalysis für Fortgeschrittene: Hier erfahren Sie alles über Topologie, lineare Operatoren, die Gelfandsche Theorie kommutativer Banach-Algebren und vieles andere. Mit durchgerechneten Beispielen und Übungsaufgaben!

Produktbeschreibung
Funktionalanalysis für Fortgeschrittene: Hier erfahren Sie alles über Topologie, lineare Operatoren, die Gelfandsche Theorie kommutativer Banach-Algebren und vieles andere. Mit durchgerechneten Beispielen und Übungsaufgaben!
  • Produktdetails
  • Wiley Series in Pure and Applied Mathematics
  • Verlag: Wiley & Sons
  • Seitenzahl: 604
  • Erscheinungstermin: 21. März 2002
  • Englisch
  • Abmessung: 243mm x 161mm x 34mm
  • Gewicht: 972g
  • ISBN-13: 9780471556046
  • ISBN-10: 0471556041
  • Artikelnr.: 10538548
Autorenporträt
P. D. Lax, Courant Institute of Mathematical Sciences, New York Univ., New York, New York
Inhaltsangabe
Foreword.
Linear Spaces.
Linear Maps.
The Hahn-Banach Theorem.
Applications of the Hahn-Banach Theorem.
Normed Linear Spaces.
Hilbert Space.
Applications of Hilbert Space Results.
Duals of Normed Linear Space.
Applications of Duality.
Weak Convergence.
Applications of Weak Convergence.
The Weak and Weak Topologies.
Locally Convex Topologies and the Krein-Milman Theorem.
Examples of Convex Sets and their Extreme Points.
Bounded Linear Maps.
Examples of Bounded Linear Maps.
Banach Algebras and their Elementary Spectral Theory.
Gelfand's Theory of Commutative Banach Algebras.
Applications of Gelfand's Theory of Commutative Banach Algebras.
Examples of Operators and their Spectra.
Compact Maps.
Examples of Compact Operators.
Positive Compact Operators.
Fredholm's Theory of Integral Equations.
Invariant Subspaces.
Harmonic Analysis on a Halfline.
Index Theory.
Compact Symmetric Operators in Hilbert Space.
Examples of Compact Symmetric Operators.
Trace Class and Trace Formula.
SpectralTheory of Symmetric, Normal and Unitary Operators.
Spectral Theory of Self-Adjoint Operators.
Examples of Self-Adjoint Operators.
Semigroups of Operators.
Groups of Unitary Operators.
Examples of Strongly Continuous Semigroups.
Scattering Theory.
A Theorem of Beurling.
Appendix A: The Riesz-Kakutani Representation Theorem.
Appendix B: Theory of Distributions.
Appendix C: Zorn's Lemma.
Author Index.
Subject Index.
Rezensionen
"...an excellent source of facts for anyone working in functional analysis or operator theory." (Journal of Operator Theory, Vol.53, No.1, 2005)

"For years Lax has been counted among the world's very top people in PDEs, so no serious student can afford to ignore his view of the foundations leading up to that subject." (Choice, Vol. 40, No. 4, December 2002)

"...attractive...well suited for graduate courses...and useful for research mathematicians." (Mathematical Reviews, 2003a)

"...The book is highly recommended to all students of analysis". (Zentralblatt MATH, Vol.1009, No.9, 2003)

"A lot of good material, doled out in short chapters." (American Mathematical Monthly, August/September 2003)