English

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{\sf A} (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 B{\sf B} is always of type A{\sf A}. 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 A{\sf A} if and only if it is of type C{\sf C} (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.

Keywords

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

R2 v1 2026-06-22T12:35:22.803Z