ABSTRACT

Presenting excellent material for a first course on functional analysis , Functional Analysis in Applied Mathematics and Engineering concentrates on material that will be useful to control engineers from the disciplines of electrical, mechanical, and aerospace engineering.

This text/reference discusses:

  • rudimentary topology
  • Banach's fixed point theorem with applications
  • L^p-spaces
  • density theorems for testfunctions
  • infinite dimensional spaces
  • bounded linear operators
  • Fourier series
  • open mapping and closed graph theorems
  • compact and differential operators
  • Hilbert-Schmidt operators
  • Volterra equations
  • Sobolev spaces
  • control theory and variational analysis
  • Hilbert Uniqueness Method
  • boundary element methods

    Functional Analysis in Applied Mathematics and Engineering begins with an introduction to the important, abstract basic function spaces and operators with mathematical rigor, then studies problems in the Hilbert space setting. The author proves the spectral theorem for unbounded operators with compact inverses and goes on to present the abstract evolution semigroup theory for time dependent linear partial differential operators. This structure establishes a firm foundation for the more advanced topics discussed later in the text.
  • chapter 1|10 pages

    Topological and Metric Spaces

    chapter 2|12 pages

    Banach Spaces

    chapter 3|10 pages

    Bounded Operators

    chapter 4|22 pages

    Hilbert Spaces.

    chapter 5|22 pages

    Operators on Hilbert Spaces

    chapter 6|14 pages

    Spectral Theory

    chapter 7|10 pages

    Integral Operators

    chapter 8|10 pages

    Semigroups of Evolution

    chapter 9|16 pages

    Sobolev Spaces

    chapter 10|13 pages

    Interpolation Spaces

    chapter 12|35 pages

    Regularity of Hyperbolic Mixed Problems

    chapter 13|35 pages

    The Hilbert Uniqueness Method