Polyharmonicity and algebraic support of measures

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Title: Polyharmonicity and algebraic support of measures
Authors: Kounchev, Ognyan
Render, Hermann
Permanent link: http://hdl.handle.net/10197/5511
Date: Feb-2007
Abstract: Our main result states that two signed measures μ and ν with bounded support contained in the zero set of a polynomial P(χ) are equal if they coincide on the subspace of all polynomials of polyharmonic degree NP where the natural number NP is explicitly computed by the properties of the polynomial P(χ). 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.
Type of material: Journal Article
Publisher: Hiroshima University. Department of Mathematics.
Journal: Hiroshima Mathematical Journal
Volume: 37
Issue: 1
Start page: 1
End page: 143
Copyright (published version): 2007 Hiroshima University. Department of Mathematics.
Keywords: PolynomialsPolyharmonic function
Other versions: http://projecteuclid.org/euclid.hmj/1176324093
Language: en
Status of Item: Peer reviewed
Appears in Collections:Mathematics and Statistics Research Collection

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