Submission date: 30 August 2023

Abstract:

We enrich the class of power-constructible functions, introduced in [CCRS23], to a class of algebras of functions which contains all complex powers of subanalytic functions, their parametric Mellin and Fourier transforms, and which is stable under parametric integration. By describing a set of generators of a special prepared form we deduce information on the asymptotics and on the loci of integrability of the functions of the class. We furthermore identify a subclass which is the smallest class containing all power-constructible functions and stable under parametric Fourier transforms and right-composition with subanalytic maps. This subclass is also stable under parametric integration, under taking pointwise and L^p-limits, and under parametric Fourier-Plancherel transforms. Finally, we give a full asymptotic expansion in the power-logarithmic scale, uniformly in the parameters, for functions in this subclass.

Mathematics Subject Classification: 26B15, 14P15, 32B20, 42B20, 42A38 (Primary) 03C64, 14P10, 33B10 (Secondary)

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Full text arXiv 2308.15958: pdf, ps.