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Uniqueness and nonuniqueness in mean boundary value problems

Published online by Cambridge University Press:  17 April 2009

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

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We give some sufficient conditions to guarantee the uniqueness of certain mean boundary value problems for a circle. Also we show that, in general, we cannot expect uniqueness of the problem for an arc unless the function is analytic in a neighborhood of the unit circle or some shifted means of the function are also known.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 8 , Issue 1 , February 1973 , pp. 23 - 26
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]Patil, D.J., “Representation of Hp functions”, Bull. Amer. Math. Soc. 78 (1972), 617–620.CrossRefGoogle Scholar