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Uniqueness and representation of a function in terms of its translated averages

Published online by Cambridge University Press:  17 April 2009

Chin-Hung Ching
Chin-Hung Ching
Affiliation:
Department of Mathematics, Texas A&M University, College Station, Texas, USA.
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Abstract

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We give the representation formula of a periodic function with period one in terms of its translated means on the unit interval. We also give an application of this formula to a boundary value problem.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 9 , Issue 1 , August 1973 , pp. 121 - 125
Copyright
Copyright © Australian Mathematical Society 1973

References

[1]Ching, Chin-Hung and Chui, Charles K., “Representation of a function in terms of its mean boundary values”. Bull. Austral. Math. Soc. 7 (1972), 425–427.CrossRefGoogle Scholar
[2]Ching, Chin-Hung and Chui, Charles K., “Uniqueness and nonuniqueness in mean boundary value problems”, Bull. Austral. Math. Soc. 8 (1973), 23–26.CrossRefGoogle Scholar
[3]Ching, Chin-Hung and Chui, Charles K., “Analytic functions characterized by their means on an arc”, Trans. Amer. Math. Soc. (to appear).Google Scholar
[4]Ching, Chin-Hung and Chui, Charles K., “Asymptotic similarities of Fourier and Riemann coefficients”, J. Approximation Theory (to appear).Google Scholar
[5]Ching, Chin-Hung and Chui, Charles K., “Mean boundary value problems and Riemann series”, J. Approximation Theory (to appear).Google Scholar
[6]Ching, Chin-Hung and Chui, Charles K., “Uniqueness theorems determined by function values at the roots of unity”, J. Approximation Theory (to appear).Google Scholar
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