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Functional Analysis in Applied Mathematics and Engineering





ISBN 9780367399412
Published June 19, 2019 by CRC Press
312 Pages

 
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Book Description

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.
  • Table of Contents

    Topological and Metric Spaces
    Banach Spaces
    Bounded Operators
    Hilbert Spaces
    Operators in Hilbert Space
    Spectral Theory
    Integral Operators
    Semigroups of Evolution
    Sobolev Spaces
    Interpolation Spaces
    Linear Elliptic Operators
    Regularity of Hyperbolic Mixed Problems
    The Hilbert Uniqueness Method
    Exercises
    References

    ...
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    Author(s)

    Biography

    Pedersen, Michael