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Orthogonal polynomials on Sobolev spaces: Old and new directions. (English) Zbl 0790.42015
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:
42C05 Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis
46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
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