Van der Corput lemmas for Mittag-Leffler functions. II. $α$-directions
dc.contributor.author | Ruzhansky, M | |
dc.contributor.author | Torebek, BT | |
dc.date.accessioned | 2021-07-08T09:33:47Z | |
dc.date.available | 2021-06-15 | |
dc.date.available | 2021-07-08T09:33:47Z | |
dc.date.issued | 2021-06 | |
dc.identifier.issn | 0007-4497 | |
dc.identifier.uri | https://qmro.qmul.ac.uk/xmlui/handle/123456789/72939 | |
dc.description.abstract | The paper is devoted to 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 integrals appearing in the analysis of time-fractional partial differential equations. More specifically, we study integral of the form $I_{\alpha,\beta}(\lambda)=\int_\mathbb{R}E_{\alpha,\beta}\left(i^\alpha\lambda \phi(x)\right)\psi(x)dx,$ for the range $0<\alpha\leq 2,\,\beta>0$. This extends the variety of estimates obtained in the first part, where integrals with functions $E_{\alpha,\beta}\left(i \lambda \phi(x)\right)$ have been studied. Several generalisations of the van der Corput lemmas are proved. As an application of the above results, the generalised Riemann-Lebesgue lemma, the Cauchy problem for the time-fractional Klein-Gordon and time-fractional Schr\"{o}dinger equations are considered. | en_US |
dc.publisher | Elsevier | en_US |
dc.relation.ispartof | Bulletin des Sciences Mathematiques | |
dc.rights | This item is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. | |
dc.rights | Attribution 3.0 United States | * |
dc.rights.uri | http://creativecommons.org/licenses/by/3.0/us/ | * |
dc.subject | math.FA | en_US |
dc.subject | math.FA | en_US |
dc.title | Van der Corput lemmas for Mittag-Leffler functions. II. $α$-directions | en_US |
dc.type | Article | en_US |
dc.rights.holder | © 2021 The Authors. Published by Elsevier Masson SAS. | |
pubs.author-url | http://arxiv.org/abs/2005.04546v1 | en_US |
pubs.notes | Not known | en_US |
pubs.publication-status | Accepted | en_US |
dcterms.dateAccepted | 2021-06-15 | |
rioxxterms.funder | Default funder | en_US |
rioxxterms.identifier.project | Default project | en_US |
Files in this item
This item appears in the following Collection(s)
-
Mathematics [1463]
Except where otherwise noted, this item's license is described as This item is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.