Fourth order partial differential equations for Krall-type orthogonal polynomials on the triangle

Delgado, Antonia; Fernández, Lidia; Pérez, Teresa

doi:10.1090/proc/14052

Fourth order partial differential equations for Krall-type orthogonal polynomials on the triangle
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by Antonia M. Delgado, Lidia Fernández and Teresa E. Pérez PDF

Proc. Amer. Math. Soc. 146 (2018), 3961-3974 Request permission

Abstract:

We construct bivariate polynomials orthogonal with respect to a Krall-type inner product on the triangle defined by adding Krall terms over the border and the vertexes to the classical inner product. We prove that these Krall-type orthogonal polynomials satisfy fourth order partial differential equations with polynomial coefficients, as an extension of the classical theory introduced by H. L. Krall in the 1940s.

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