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Zbl 0790.42015
Marcellán, F.; Alfaro, M.; Rezola, M.L.
Orthogonal polynomials on Sobolev spaces: Old and new directions. (English)
[J] J. Comput. Appl. Math. 48, No.1-2, 113-131 (1993). ISSN 0377-0427

Summary: During the last years, orthogonal polynomials on Sobolev spaces have attracted considerable attention. Algebraic properties, distribution of their zeros, and Fourier expansions as well as their relevance in the analysis of spectral methods for partial differential equations provide a very large field to explore and to compare with the standard case. In this paper we present an introductory survey about the subject. The origin of the problems and their development show the interest and the promising future of this field.

MSC 2000:: *42C05 General theory of orthogonal functions and polynomials
46E35 Sobolev spaces and generalizations

Keywords: Sobolev inner product; recurrence relations; orthogonal polynomials; Sobolev spaces; zeros; Fourier expansions; spectral methods; partial differential equations; introductory survey

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Zentralblatt MATH Berlin [Germany]