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arXiv · 1605.09665

Approximation in M\"untz spaces $M_{\Lambda ,p}$ of $L_p$ functions for $1<p<\infty $ and bases

Sergey V. Ludkowski
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Abstract

M\"untz spaces satisfying the M\"untz and gap conditions are considered. A Fourier approximation of functions in the M\"untz spaces $M_{\Lambda ,p}$ of $L_p$ functions is studied, where $1<p<\infty $. It is proved that up to an isomorphism and a change of variables these spaces are contained in Weil-Nagy's class. Moreover, existence of Schauder bases in the M\"untz spaces $M_{\Lambda ,p}$ is investigated.

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Sergey V. Ludkowski. 2016-05-31. Approximation in M\"untz spaces $M_{\Lambda ,p}$ of $L_p$ functions for $1<p<\infty $ and bases. https://doi.org/10.3390/math5010010

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