Multiplicity of zeros and discrete orthogonal polynomials

Ilia Krasikov

doi:10.1007/BF03322997

Multiplicity of zeros and discrete orthogonal polynomials

Ilia Krasikov^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

Abstract

We consider a problem of bounding the maximal possible multiplicity of a zero of some expansions Σ a_iF_i(x), at a certain point c, depending on the chosen family {imi}. 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.

Original language	English
Pages (from-to)	59-66
Number of pages	8
Journal	Results in Mathematics
Volume	45
Issue number	1-2
DOIs	https://doi.org/10.1007/BF03322997
State	Published - 1 Mar 2004
Externally published	Yes

Keywords

Classical Orthogonal Polynomial
Distance Distribution
Laguerre Polynomial
Orthogonal Polynomial
Prescribe Norm

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10.1007/BF03322997

Cite this

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KW - Orthogonal Polynomial

KW - Prescribe Norm

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Multiplicity of zeros and discrete orthogonal polynomials

Abstract

Keywords

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