Polyharmonicity and algebraic support of measures
Kounchev, Ognyan ; Render, Hermann
Hiroshima Math. J., Tome 37 (2007) no. 1, p. 25-44 / Harvested from Project Euclid
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/