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arXiv · 2105.09552

On almost everywhere convergence of Malmquist-Takenaka series

Gevorg Mnatsakanyan
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Abstract

The Malmquist-Takenaka system is a perturbation of the classical trigonometric system, where powers of $z$ are replaced by products of other M\"obius transforms of the disc. The system is also inherently connected to the so-called nonlinear phase unwinding decomposition which has been in the center of some recent activity. We prove $L^p$ bounds for the maximal partial sum operator of the Malmquist-Takenaka series under additional assumptions on the zeros of the M\"obius transforms. We locate the problem in the time-frequency setting and, in particular, we connect it to the polynomial Carleson theorem.

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BibTeXRIS

Gevorg Mnatsakanyan. 2021-05-20. On almost everywhere convergence of Malmquist-Takenaka series. https://doi.org/10.1016/j.jfa.2022.109461

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