Integral equations
著者
書誌事項
Integral equations
（Cambridge tracts in mathematics and mathematical physics, no. 49）
Cambridge University Press, 2008
Digitally printed version
- : pbk
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注記
Originally published: 1958
Includes bibliographical references and index
内容説明・目次
内容説明
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.
目次
- 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.
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