Polyharmonicity and algebraic support of measures

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概要

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• 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.

• 広島大学の論文

著者

• Hermann Render

  Departamento De Mathematicas Y Computation Universidad De La Rioja

• Ognyan Kounchev

  Institute of Mathematics and Informatics, Bulgarian Academy of Sciences

• Ognyan Kounchev

  Institute Of Mathematics And Informatics Bulgarian Academy Of Sciences

関連論文

• Polyharmonicity and algebraic support of measures

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