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Polyharmonicity and algebraic support of measures
Author(s)
Date Issued
2007-02
Date Available
2014-04-01T08:34:23Z
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.
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.
Web versions
Language
English
Status of Item
Peer reviewed
This item is made available under a Creative Commons License
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HiroshimaProofs0307.pdf
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