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A Cohen type inequality for Fourier expansions of orthogonal polynomials with a non-discrete Gegenbauer-Sobolev inner product. (English) Zbl 1210.42042

The author considers polynomials which are orthogonal with respect to a non-discrete Gegenbauer -Sobolev inner product. These polynomials constitute a particular case of the so-called symmetrically coherent pairs of measures, studied by H.G. Meijer [J. Approx. Theory 89, 321–343 (1997; Zbl 0880.42012)]. The author obtains estimates and asymptotics for the above polynomials as well as for their first derivative and the main result of the paper is a Cohen-type inequality for Fourier expansions in terms of these polynomials.

MSC:

42C05 Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis
42C10 Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.)
33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.)

Citations:

Zbl 0880.42012
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References:

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