Talk: Sobolev orthogonal polynomials: connection formulas and zeros

Date: 2024..06..27
Event: IMAG Conference on Orthogonal Polynomials, Special Functions and Applications - OPSFA17
Venue: Granada, Spain

Abstract

This contribution aims to obtain several connection formulae for the polynomial sequence, which is orthogonal with respect to the discrete Sobolev inner product \[ \langle f, g\rangle_n=\langle {\bf u}, fg\rangle+ \sum_{j=1}^M \mu_{j} f^{(\nu_j)}(c_j) g^{(\nu_j)}(c_j), \] where \({\bf u}\) is a classical linear functional, \(c_j\in \mathbb R, \nu_j\in \mathbb N_0, j=1, 2,...., M\).

We later consider the \(M=2\) case, we take the linear Krawtchouk functional \({\bf u}^{\tt K}\), and assume that we have two mass points that can be either outside or inside the convex hull of the support of \({\bf u}^{\tt K}\), and briefly study the behavior of the zeros of the Krawtchouk-Sobolev polynomials, which are orthogonal with respect to the said inner product, in different situations.

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