Differential orthogonality: Laguerre and Hermite cases with applications

Author(s)

Borrego-Morell, J. ^[1] ; Pijeira-Cabrera, H. ^[2]

Affiliation

^[1] Univ Estadual Paulista, UNESP, IBILCE, Sao Paulo - Brazil

^[2] Univ Carlos III Madrid, E-28903 Getafe - Spain

• Document type: Journal article
• Source: Journal of Approximation Theory; v. 196, p. 111-130, AUG 2015.
• Web of Science Citations: 0

Abstract

Let mu be a finite positive Borel measure supported on R, L{[}f] = xf `' + (alpha +1 - x)f' with alpha > -1, or L{[}f] = 1/2f `' - xf', and m a natural number. We study algebraic, analytic and asymptotic properties of the sequence of monic polynomials [Q(n)](n>m) that satisfy the orthogonality relations integral L{[}Q(n)](x)x(k)d mu(x) = 0 for all 0 <= k <= n - 1. We also provide a fluid dynamics model for the zeros of these polynomials. (C) 2015 Elsevier Inc. All rights reserved. (AU)

• FAPESP's process: 12/21042-0 - Orthogonal polynomials with respect to differential operators and matrix orthogonal polynomials
• Grantee: Jorge Alberto Borrego Morell
• Support Opportunities: Scholarships in Brazil - Post-Doctoral