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arXiv · 1902.09466

Double bases from generalized Faber polynomials with complex-valued coefficients in weighted Lebesgue spaces

B. T. Bilalov·A. A. Huseynli·S. R. Sadigova
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Abstract

In the paper it is considered the generalized Faber polynomials defined inside and outside a regular curve on the complex plane. The weighted Smirnov spaces corresponding to bounded and unbounded regions are defined. It is proved that the generalized Faber polynomials forms a basis in weighted Smirnov spaces, if the weight function satisfies the Muckenhoupt condition on the regular curve. The double system of generalized Faber polynomials with complex-valued coefficients is also considered and the basis properties of such a system in weighted Lebesgue spaces over regular curves are studied.

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B. T. Bilalov, A. A. Huseynli, S. R. Sadigova. 2019-02-25. Double bases from generalized Faber polynomials with complex-valued coefficients in weighted Lebesgue spaces. https://arxiv.org/abs/1902.09466

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