Integral Equations

This tract is devoted to the theory of linear equations, mainly of the second kind, associated with the names of Volterra, Fredholm, Hilbert and Schmidt.

Smithies (Author)

9780521100038, Cambridge University Press

Paperback / softback, published 18 January 2009

188 pages
21.6 x 14 x 1.1 cm, 0.24 kg

This tract is devoted to the theory of linear equations, mainly of the second kind, associated with the names of Volterra, Fredholm, Hilbert and Schmidt. The treatment has been modernised by the systematic use of the Lebesgue integral, which considerably widens the range of applicability of the theory. Special attention is paid to the singular functions of non-symmetric kernels and to obtaining as strong results as possible for the convergence of the expansions in infinite series. References are given to work on numerical methods of solution. Individual chapters deal with the resolvent kernel and the Neumann series, the Fredholm theorems, orthonormal systems of functions, the classical Fredholm theory, the Fred-holm formulae for ß2 kernels, Hermitian kernels, singular functions and singular values.

1. Introduction
2. The Resolvent Kernel and the Neumann Series
3. The Fredholme Theorems
4. Orthonormal Systems of Functions
5. The Classical Fredholme Theory
6. The Fredholme Formulae for ß2 kernels
7. Hermitian kernels
8. Singular Functions and Singular Values.

Subject Areas: Mathematics [PB]