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Applications of the monotonicity of extremal zeros of orthogonal polynomials in interlacing and optimization problems |
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| Authors: | Wolfgang Erb |
| Institution: | a Institute of Mathematics, University of Lübeck, Wallstrasse 40, 23560 Lübeck, Germany b Institute for Biomathematics and Biometry, Helmholtz Center Munich, Ingolstädter, Landstrasse 1, 85764 Neuherberg, Germany |
| Abstract: | We investigate monotonicity properties of extremal zeros of orthogonal polynomials depending on a parameter. Using a functional analysis method we prove the monotonicity of extreme zeros of associated Jacobi, associated Gegenbauer and q-Meixner-Pollaczek polynomials. We show how these results can be applied to prove interlacing of zeros of orthogonal polynomials with shifted parameters and to determine optimally localized polynomials on the unit ball. |
| Keywords: | Monotonicity of zeros Associated Jacobi polynomials Associated Gegenbauer polynomials q-Meixner-Pollaczek polynomials Interlacing of zeros Orthogonal polynomials on the unit ball |
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