English

Multiplicity of zeros and discrete orthogonal polynomials

Classical Analysis and ODEs 2016-09-07 v1

Abstract

We consider a problem of bounding the maximal possible multiplicity of a zero at of some expansions aiFi(x)\sum a_i F_i(x), at a certain point c,c, depending on the chosen family {Fi}\{F_i \}. The most important example is a polynomial with c=1.c=1. It is shown that this question naturally leads to discrete orthogonal polynomials. Using this connection we derive some new bounds, in particular on the multiplicity of the zero at one of a polynomial with a prescribed norm.

Keywords

Cite

@article{arxiv.math/0204317,
  title  = {Multiplicity of zeros and discrete orthogonal polynomials},
  author = {Ilia Krasikov},
  journal= {arXiv preprint arXiv:math/0204317},
  year   = {2016}
}