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A Kolmogorov-Szegö-Krein type condition for weighted Sobolev spaces. (English) Zbl 1074.41004

An analogue of the Szegő condition for density of analytic polynomials in a weighted Sobolev space \( W^{k,p}\) of the circle with general weights is given here. This work of the authors is particularly close to questions studied in [J. A. Ball and T. R. Fanney, J. Oper. Theory 33, 43–78 (1995; Zbl 0849.47011)]. It is also observed that the solution of the question of density of analytic polynomials in weighted Sobolev spaces is of importance in the theory of sub-Jordan operators.

MSC:

41A10 Approximation by polynomials

Citations:

Zbl 0849.47011
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