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Van der Corput lemmas for Mittag-Leffler functions | | Michael Ruzhansky
; Berikbol T. Torebek
; | | Date: |
18 Feb 2020 | | 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. | | Source: | arXiv, 2002.7492 | | Services: | Forum | Review | PDF | Favorites | |
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