Polyharmonicity and algebraic support of measures
|Title:||Polyharmonicity and algebraic support of measures||Authors:||Kounchev, Ognyan
|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:||Polynomials; Polyharmonic 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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