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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

[1]Aljančić, S., ‘Uber Summierbarkeit Von Orthogonalentwicklungen Stetigen Funktion’, Publ. Inst. Math. Acad. Serbe Sci. X (1956), 121–130.Google Scholar
[2]Husain, Syed A., ‘On Uniform Convergence Factors of Orthonormal Expansions of Functions of Class L∞’, J. Reine Angew. Math. 238 (1969), 217–220.Google Scholar
[3]Husain, Syed A., ‘Convergence Factors of Fourier Series of Summable Functions’, J. Reine Angew. Math. 259 (1973), 183–186.Google Scholar
[4]Mukherjea, A. and Pothoven, K., Real and Functional Analysis (Plenum Press, New York and London, 1978).CrossRefGoogle Scholar