POLINOMIOS ORTOGONALES NO ESTÁNDAR. APLICACIONES EN ANÁLISIS NUMÉRICO Y TEORÍA DE LA APROXIMACIÓN

Francisco Marcellán

doi:10.18257/raccefyn.30(117).2006.2284

Vol. 30 No. 117 (2006), Mathematics

Vol. 30 No. 117 (2006)

NON-STANDARD ORTHOGONAL POLYNOMIALS. APPLICATIONS IN NUMERICAL ANALYSIS AND APPROXIMATION THEORY

Mathematics

https://doi.org/10.18257/raccefyn.30(117).2006.2284

Published 2023-11-25

Francisco Marcellán⁺⁻

Francisco Marcellán

Departamento de Matemáticas, Universidad Carlos III de Madrid. Avenida de la Universidad 30, 28911, Leganés, España.

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How to Cite

Marcellán, F. (2023). NON-STANDARD ORTHOGONAL POLYNOMIALS. APPLICATIONS IN NUMERICAL ANALYSIS AND APPROXIMATION THEORY. Revista De La Academia Colombiana De Ciencias Exactas, Físicas Y Naturales, 30(117), 563–580. https://doi.org/10.18257/raccefyn.30(117).2006.2284

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Abstract

In this contribution, we present a summary of recent results on applications of the theory of non-standard orthogonal polynomials (in particular, associated with measures supported on the unit circle and with respect to Sobolev products associated with a vector of measures supported on the real line). We consider spectral transformations of measures and their analysis from the point of view of matrix factorization. Finally, we deal with some problems of approximation theory in Sobolev spaces.

https://doi.org/10.18257/raccefyn.30(117).2006.2284

Keywords

Orthogonal polynomials | state-space generators | moment matrices | spectral

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