Abstract
A system of linear algebraic equations with a real, symmetric matrix of coefficients can be reduced to an uncoupled, immediately solvable form, by using the eigenvectors of the matrix as base vectors. In the present chapter we discuss Schmidt’s analogous representation of symmetric integral operators in terms of their eigenvalues and eigenfunctions. Because only square-integrable functions are considered, a function can be treated as a vector with an infinite number of components, and much of the theory traces back to Hilbert’s theory of infinite matrices.
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© 1991 Springer Science+Business Media New York
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Pipkin, A.C. (1991). Hilbert—Schmidt Theory. In: A Course on Integral Equations. Texts in Applied Mathematics, vol 9. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-4446-2_3
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DOI: https://doi.org/10.1007/978-1-4612-4446-2_3
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-8773-5
Online ISBN: 978-1-4612-4446-2
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