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.
Publié le : 2007-03-14
Classification:
Markov function,
Stieltjes transform,
polynomial of second kind,
polyharmonic function,
44A15,
35D55,
42C05
@article{1176324093,
author = {Kounchev, Ognyan and Render, Hermann},
title = {Polyharmonicity and algebraic support of measures},
journal = {Hiroshima Math. J.},
volume = {37},
number = {1},
year = {2007},
pages = { 25-44},
language = {en},
url = {http://dml.mathdoc.fr/item/1176324093}
}
Kounchev, Ognyan; Render, Hermann. Polyharmonicity and algebraic support of measures. Hiroshima Math. J., Tome 37 (2007) no. 1, pp. 25-44. http://gdmltest.u-ga.fr/item/1176324093/