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Applied Functional Analysis
Jean-Pierre Aubin (Author)
9780471179764, Wiley
Hardback, published 15 February 2000
520 pages
24.6 x 16.2 x 3 cm, 0.857 kg
“…full of interesting and/or amazing comments…an original and valuable contribution to functional analysis…” (Bulletin of The Belgian Mathematical Society, Vol.11, No.4, 2004) "Reflects author's background in numerical analysis, partial differential equations, and mathematical economics.... Good exercises." (American Mathematical Monthly, November 2001) "The second edition has made some additions and some deletions..." (Zentralblatt MATH, Vol. 946, No. 21)
Mit diesem Buch verfolgt der Autor zwei Ziele: Erstens will er in die wichtigsten algebraischen Strukturen einführen, zweitens will er den Studenten helfen, ihre Fähigkeiten zum Arbeiten mit abstrakten Begriffen zu vervollkommnen. Die Kerngedanken werden in den ersten sechs Kapiteln vorgestellt, während der zweite Teil des Buches flexibel angelegt ist. Didaktisch sehr sinnvoll ist die beigefügte Anleitung zum Lesen, Analysieren und Aufstellen von Sätzen und Beweisen. (12/99)
The Projection Theorem.
Theorems on Extension and Separation.
Dual Spaces and Transposed Operators.
The Banach Theorem and the Banach-Steinhaus Theorem.
Construction of Hilbert Spaces.
L¯2 Spaces and Convolution Operators.
Sobolev Spaces of Functions of One Variable.
Some Approximation Procedures in Spaces of Functions.
Sobolev Spaces of Functions of Several Variables and the Fourier Transform.
Introduction to Set-Valued Analysis and Convex Analysis.
Elementary Spectral Theory.
Hilbert-Schmidt Operators and Tensor Products.
Boundary Value Problems.
Differential-Operational Equations and Semigroups of Operators.
Viability Kernels and Capture Basins.
First-Order Partial Differential Equations.
Selection of Results.
Exercises.
Bibliography.
Index.
Subject Areas: Mathematics [PB]
