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The expansion of continuous functions in series of integrals of orthonormal functions

Published online by Cambridge University Press:  18 May 2009

H. C. Finlayson
H. C. Finlayson
Affiliation:
University of Manitoba, Manitoba, Canada
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This paper deals with the following problem: Can an arbitrary continuous function on [0, 1], which vanishes at the origin, be represented in some sense as a series of constant multiples of indefinite integrals of a complete orthonormal set of functions on [0,1]? Four contexts in which this problem arises naturally will be given in the introduction and the remainder of the paper will be devoted to giving a partial answer to the specific problem formulated in one of these contexts.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 13 , Issue 1 , March 1972 , pp. 29 - 38
Copyright
Copyright © Glasgow Mathematical Journal Trust 1972

References

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