Parametric Fourier and Mellin transforms of power-constructible functions

Cluckers, Raf; Comte, Georges; Servi, Tamara

Document type :

Pré-publication ou Document de travail

Title :

Parametric Fourier and Mellin transforms of power-constructible functions

Author(s) :

Cluckers, Raf [Auteur]

Laboratoire Paul Painlevé - UMR 8524 [LPP]
Comte, Georges [Auteur]
Servi, Tamara [Auteur]

Publication date :

2023-08-30

HAL domain(s) :

Mathématiques [math]

English abstract : [en]

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, ...
Show more >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.Show less >

Language :

Anglais

Collections :

Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL

Files

2308.15958
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