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March 2007 Polyharmonicity and algebraic support of measures
Ognyan Kounchev, Hermann Render
Hiroshima Math. J. 37(1): 25-44 (March 2007). DOI: 10.32917/hmj/1176324093


Our main result states that two signed measures $\mu$ and $\nu$ with bounded support contained in the zero set of a polynomial $P(x)$ are equal if they coincide on the subspace of all polynomials of polyharmonic degree $N_{P}$ where the natural number $N_{P}$ is explicitly computed by the properties of the polynomial $P\left( x\right) $. The method of proof depends on a definition of a multivariate Markov transform which is another major objective of the present paper. The classical notion of orthogonal polynomial of second kind is generalized to the multivariate setting: it is a polyharmonic function which has similar features to those in the one-dimensional case.


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Ognyan Kounchev. Hermann Render. "Polyharmonicity and algebraic support of measures." Hiroshima Math. J. 37 (1) 25 - 44, March 2007.


Published: March 2007
First available in Project Euclid: 11 April 2007

zbMATH: 1124.44003
MathSciNet: MR2308522
Digital Object Identifier: 10.32917/hmj/1176324093

Primary: 44A15
Secondary: 35D55, 42C05

Rights: Copyright © 2007 Hiroshima University, Mathematics Program


Vol.37 • No. 1 • March 2007
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