Algebraic sets of types A, B, and C coincide
Functional Analysis
2016-01-26 v1
Abstract
It is proved that the definition of an algebraic set of type (a notion related to the multidimensional Hamburger moment problem) does not depend on the choice of a polynomial describing the algebraic set in question and that an algebraic set of type is always of type . This answers in the affirmative two questions posed in 1992 by the second author. It is also shown that an algebraic set is of type if and only if it is of type (a notion linked to orthogonality of polynomials of several variables). This, in turn, enables us to answer three questions posed in 2005 by Cicho\'n, Stochel, and Szafraniec.
Cite
@article{arxiv.1601.06264,
title = {Algebraic sets of types A, B, and C coincide},
author = {Torben Maack Bisgaard and Jan Stochel},
journal= {arXiv preprint arXiv:1601.06264},
year = {2016}
}
Comments
The paper was written in December 2007 and not published anywhere else