Applied Functional Analysis, 2nd Edition

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.