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Jacobi series which converge to zero, with applications to a class of singular partial differential equations

Published online by Cambridge University Press:  24 October 2008

Jet Wimp  and
David Colton
Jet Wimp
Affiliation:
Midwest Research Institute, Kansas City; The University, Edinburgh
David Colton
Affiliation:
Midwest Research Institute, Kansas City; The University, Edinburgh
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Extract

Expansions in series of functions are one of the most important tools of the applied mathematician, particularly expansions in series of the classical orthogonal polynomials, e.g. Laguerre, Jacobi and Hermite polynomials. In applied problems, the uniqueness of the particular expansion is usually intrinsic to the analysis, and often implicitly assumed. Indeed, in those cases where the functions in the series are orthogonal, uniqueness can often be proved by an argument that runs as follows. Let {φn(x)} (n = 0, 1, 2, …) be a sequence of functions orthogonal with respect to the weight function ρ(x) over the interval [0, 1], and suppose that

the series being boundedly convergent for 0 ≤ x ≤ 1.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 65 , Issue 1 , January 1969 , pp. 101 - 106
Copyright
Copyright © Cambridge Philosophical Society 1969

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References

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