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Asymptotics and Confluence for Some Linear q-Difference–Differential Cauchy Problem

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Abstract

A linear Cauchy problem with polynomial coefficients which combines \(q-\)difference operators for \(q>1\) and differential operators of irregular type is examined. A finite set of sectorial holomorphic solutions w.r.t the complex time is constructed by means of classical Laplace transforms. These functions share a common asymptotic expansion in the time variable which turns out to carry a double-layer structure which couples \(q-\)Gevrey and Gevrey bounds. In the last part of the work, the problem of confluence of these solutions as \(q \rightarrow 1\) is investigated.

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  1. Laboratoire Paul Painlevé, University of Lille, 59655, Villeneuve d’Ascq Cedex, France

    S. Malek

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  1. S. Malek
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Malek, S. Asymptotics and Confluence for Some Linear q-Difference–Differential Cauchy Problem. J Geom Anal 32, 93 (2022). https://doi.org/10.1007/s12220-021-00820-z

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