Interlacing properties of zeros of multiple orthogonal polynomials
Copyright policy )Interlacing properties of zeros of multiple orthogonal polynomials
It is well known that the zeros of orthogonal polynomials interlace. In this paper we study the case of multiple orthogonal polynomials. We recall known results and some recursion relations for multiple orthogonal polynomials. Our main result gives a sufficient condition, based on the coefficients in the recurrence relations, for the interlacing of the zeros of neighboring multiple orthogonal polynomials. We give several examples illustrating our result.
18 pages
- Katholieke Universiteit Leuven Belgium
- KU Leuven Belgium
Mathematics - Classical Analysis and ODEs, Applied Mathematics, Recurrence relations, Multiple orthogonal polynomials, Classical Analysis and ODEs (math.CA), FOS: Mathematics, 33C47, 42C05, 65Q30, 26C10, Interlacing zeros, Analysis
Mathematics - Classical Analysis and ODEs, Applied Mathematics, Recurrence relations, Multiple orthogonal polynomials, Classical Analysis and ODEs (math.CA), FOS: Mathematics, 33C47, 42C05, 65Q30, 26C10, Interlacing zeros, Analysis
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