Van der Corput lemmas for Mittag-Leffler functions. I
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arXiv
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| Format: | Preprint |
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2020
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| _version_ | 1866910573963247616 |
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| author | Ruzhansky, Michael Torebek, Berikbol T. |
| author_facet | Ruzhansky, Michael Torebek, Berikbol T. |
| contents | 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 Schrödinger equation are considered. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2002_07492 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Van der Corput lemmas for Mittag-Leffler functions. I Ruzhansky, Michael Torebek, Berikbol T. Functional Analysis 42B20, 33E12 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 Schrödinger equation are considered. |
| title | Van der Corput lemmas for Mittag-Leffler functions. I |
| topic | Functional Analysis 42B20, 33E12 |
| url | https://arxiv.org/abs/2002.07492 |