A moment problem on Jordan domains
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- by Makoto Sakai PDF
- Proc. Amer. Math. Soc. 70 (1978), 35-38 Request permission
Abstract:
Let ${D_1},{D_2}$ be Jordan domains on the complex z-plane such that ${\smallint _{{D_1}}}{z^n}dm = {\smallint _{{D_2}}}{z^n}dm$ for every nonnegative integer n. Here m denotes two-dimensional Lebesgue measure. Does it follow that ${D_1} = {D_2}$? This moment problem on Jordan domains was posed by H. S. Shapiro [2, p. 193, Problem 1]. In this paper we construct a counterexample and study conditions on ${D_1}$ and ${D_2}$ which imply that the above equality does not hold for some n.References
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Additional Information
- © Copyright 1978 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 70 (1978), 35-38
- MSC: Primary 30A80
- DOI: https://doi.org/10.1090/S0002-9939-1978-0470216-5
- MathSciNet review: 0470216