New steps on Sobolev orthogonality in two variables

Sobolev orthogonal polynomials in two variables are defined via inner products involving gradients. Such a kind of inner product appears in connection with several physical and technical problems. Matrix second-order partial differential equations satisfied by Sobolev orthogonal polynomials are stud...

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Veröffentlicht in:	Journal of computational and applied mathematics 2010-12, Vol.235 (4), p.916-926
Hauptverfasser:	Bracciali, Cleonice F., Delgado, Antonia M., Fernández, Lidia, Pérez, Teresa E., Piñar, Miguel A.
Format:	Artikel
Sprache:	eng
Schlagworte:	Classical orthogonal polynomials Computation Exact sciences and technology Fourier analysis Functional analysis Functionals Joints Mathematical analysis Mathematical models Mathematics Numerical analysis Numerical analysis. Scientific computation Operators Orthogonal polynomials in two variables Orthogonality Partial differential equations Partial differential equations, initial value problems and time-dependant initial-boundary value problems Sciences and techniques of general use Sobolev orthogonal polynomials Special functions
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Beschreibung
Zusammenfassung:	Sobolev orthogonal polynomials in two variables are defined via inner products involving gradients. Such a kind of inner product appears in connection with several physical and technical problems. Matrix second-order partial differential equations satisfied by Sobolev orthogonal polynomials are studied. In particular, we explore the connection between the coefficients of the second-order partial differential operator and the moment functionals defining the Sobolev inner product. Finally, some old and new examples are given.
ISSN:	0377-0427 1879-1778
DOI:	10.1016/j.cam.2010.07.006