Lectures on Integral Equations

Front Cover
Dover Publications, 1969 - Mathematics - 124 pages

This concise and classic volume presents the main results of integral equation theory as consequences of the theory of operators on Banach and Hilbert spaces. In addition, it offers a brief account of Fredholm's original approach. The self-contained treatment requires only some familiarity with elementary real variable theory, including the elements of Lebesgue integration, and is suitable for advanced undergraduates and graduate students of mathematics.
Other material discusses applications to second order linear differential equations, and a final chapter uses Fourier integral techniques to investigate certain singular integral equations of interest for physical applications as well as for their own sake. A helpful index concludes the text.
Dover (2016) corrected republication of the edition originally published by the Van Nostrand Reinhold Co., New York, 1969.
www.doverpublications.com

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Contents

Banach Spaces
5
Completely Continuous Operators
15
Hilbert Space Theory
45
Copyright

2 other sections not shown

Other editions - View all

Lectures on Integral Equations
Harold Widom
Limited preview - 2016
Lectures on Integral Equations
Harold Widom
Limited preview - 2016

Common terms and phrases

a₁ analytic assume B₁ Banach space belongs to L₂ boundary conditions Chapter closed subspace complete orthogonal completely continuous operators complex numbers define Definition eigenfunction of G eigenvalue eigenvectors En+1 equation Tx equivalent f y)dy finite dimensional follows Fourier transform Fredholm Green's function half-plane Hence Hermitian Hilbert problem Hilbert space Hilbert transform Hilbert-Schmidt implies inner product integral equation integral operator L₁ L₂ L₂[a lemma Let F Let Te L(E linear functional linear transformation Mercer's Theorem null space obtain one-one operator with kernel orthonormal basis Parseval's identity Proof prove Remark resolvent set satisfies self-adjoint sequence series converges spectral radius spectrum step functions subspace of H Theorem tion unique solution vanishes vector Volterra whence Wiener-Hopf x)dx y)dz y₁ zero α α αξ λφ

About the author (1969)

Harold Widom is Professor Emeritus of Mathematics at the University of California, Santa Cruz. His other Dover book is Lectures on Integral Equations.

Bibliographic information

TitleLectures on Integral Equations
Dover Books on Mathematics
Issue 17 of Van Nostrand mathematical studies, ISSN 0083-5145
AuthorHarold Widom
PublisherDover Publications, 1969
Original fromthe University of Michigan
DigitizedFeb 5, 2010
ISBN0486817822, 9780486817828
Length124 pages
Subjects › 

Mathematics / Complex Analysis
Mathematics / Functional Analysis
  
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