Multiplicity of zeros and discrete orthogonal polynomials
Copyright policy )Multiplicity of zeros and discrete orthogonal polynomials
We consider a problem of bounding the maximal possible multiplicity of a zero at of some expansions $\sum a_i F_i(x)$, 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.
- Universiti Brunei Darussalam Brunei Darussalam
Mathematics - Classical Analysis and ODEs, Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral), multiplicity of zeros, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Other special orthogonal polynomials and functions, orthogonal polynomials, 30C15, 33C47
Mathematics - Classical Analysis and ODEs, Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral), multiplicity of zeros, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Other special orthogonal polynomials and functions, orthogonal polynomials, 30C15, 33C47
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