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Orthonormal expansions and the principle of uniform boundedness

Published online by Cambridge University Press:  17 April 2009

S.A. Husain  and
V.M. Sehgal
S.A. Husain
Affiliation:
Department of Mathematics, University of Wyoming Laramie, Wyoming 82071, United States of America
V.M. Sehgal
Affiliation:
Department of Mathematics, University of Wyoming Laramie, Wyoming 82071, United States of America
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Abstract

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Let {φν: ν ∈ N (non-negative integers)} ⊆ C[0, 1] be a complete orthonormal sequence of complex-valued functions in L2[0, 1], {λν: ν ∈ N} and {λνμ: ν, μ ∈ N} be sequences of complex numbers. In this paper, the necessary and sufficient conditions are developed for the series to converge and also to exist, in C[0, 1] for each f ∈ L1[0, 1] where .

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 43 , Issue 2 , April 1991 , pp. 341 - 347
Copyright
Copyright © Australian Mathematical Society 1991

References

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