Parametric Fourier and Mellin transforms of power-constructible functions

Cluckers, Raf; Comte, Georges; Servi, Tamara

Type de document :

Pré-publication ou Document de travail

Titre :

Parametric Fourier and Mellin transforms of power-constructible functions

Auteur(s) :

Cluckers, Raf [Auteur]

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

Date de publication :

2023-08-30

Discipline(s) HAL :

Mathématiques [math]

Résumé en anglais : [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, ...
Lire la suite >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.Lire moins >

Langue :

Anglais

Collections :

Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL

Fichiers

2308.15958
Accès libre
Accéder au document

Parametric Fourier and Mellin transforms ... BibTeX CSV Excel RIS

Fichiers

Parametric Fourier and Mellin transforms ...

BibTeX

CSV

Excel

RIS