Multiplicity of zeros and discrete orthogonal polynomials

2002/04/25 by Ilia Krasikov, Krasikov, Ilia
Mathematics · #30C15 #33C47 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #math.CA #msc:30C15 #msc:33C47

paper · pdf · doi:10.48550/arxiv.math/0204317

arxiv created 2002/04/25 · arxiv updated 2016/09/07

Abstract

We consider a problem of bounding the maximal possible multiplicity of a zero at of some expansions ∑ a_i F_i(x), at a certain point c, depending on the chosen family \F_i \. The most important example is a polynomial with 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.

Related

• More results on the number of zeros of multiplicity at least r
• Bounds for extreme zeros of some classical orthogonal polynomials
• On the number of zeros of multiplicity r
• On discrete orthogonal polynomials of several variables
• On the multiplicity of solutions of a system of algebraic equations