 1579 Stephane Malek
 On parametric Gevrey asymptotics for a qanalog of some linear initial value problem
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Aug 13, 15

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Abstract. We study an inhomogeneous linear qdifference differential Cauchy problem, with a complex perturbation parameter. This problem is seen as a qanalog of an initial value problem recently investigated by the author and A. Lastra. Here a comparable
result is achieved, namely we construct a finite set of holomorphic solutions on a common bounded open sector in time at the origin, on a given strip in space, when the parameter belongs to a well selected set of open bounded sectors whose union covers a neighborhood of 0 in the complex domain. These solutions are constructed through a continuous version of a qLaplace transform of some order k and Fourier inverse map of some function with qexponential growth of order k on adequate unbounded sectors and with exponential decay in the Fourier
variable. Moreover, by means of a qanalog of the classical RamisSibuya theorem, we prove that they share a common formal power series
(that generally diverge) in the perturbation parameter as qGevrey asymptotic expansion of order 1/k.
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