Talk: Krawtchuk Sobolev polynomials. Old and new results

Date: 2022..06..02
Event: International congress COMPUMATG 2022
Venue: Universidad de Granma, Cuba

Abstract

In this talk we present different connection formulas for the Krawtchuk Sobolev polynomials which are orthogonal with respect to the inner product: \[ (f,g)_S = \langle {\bf u}, fg \rangle + \lambda \Delta^i f(c)\Delta^i g(c), \] where \({\bf u}\) is the lineal form associated to the Krawtchuk polynomials, \(i\) is a positive integer, \(\lambda, c\) are real numbers, and \(\Delta\) is the forward difference operator.

We will also show an holonomic second order difference equation that this succession of polynomials satisfies as well as a factorisation of this family of polynomials for \(n\ge N\) through which we can define a new internal product with respect to which the sequence of Krawtchuk Sobolev polynomials are orthogonal for degrees higher than \(N\).

This is a joint work with Anier Soria Lorente.

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