Functional Analysis in Applied Mathematics and Engineering: 1st Edition (Hardback) book cover

Functional Analysis in Applied Mathematics and Engineering

1st Edition

By Michael Pedersen

CRC Press

312 pages

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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

    About the Series

    Studies in Advanced Mathematics

    Learn more…

    Subject Categories

    BISAC Subject Codes/Headings:
    MAT000000
    MATHEMATICS / General
    MAT003000
    MATHEMATICS / Applied
    MAT037000
    MATHEMATICS / Functional Analysis