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arXiv · 2002.07492

Van der Corput lemmas for Mittag-Leffler functions. I

Michael Ruzhansky·Berikbol T. Torebek
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Abstract

In this paper, we study analogues of the van der Corput lemmas involving Mittag-Leffler functions. The generalisation is that we replace the exponential function with the Mittag-Leffler-type function, to study oscillatory type integrals appearing in the analysis of time-fractional partial differential equations. Several generalisations of the first and second van der Corput lemmas are proved. Optimal estimates on decay orders for particular cases of the Mittag-Leffler functions are also obtained. As an application of the above results, the generalised Riemann-Lebesgue lemma and the Cauchy problem for the time-fractional Schr\"{o}dinger equation are considered.

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Michael Ruzhansky, Berikbol T. Torebek. 2020-02-18. Van der Corput lemmas for Mittag-Leffler functions. I. https://doi.org/10.4171/zaa%2F1763

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