$q$-Analogues of Laplace and Borel transforms by means of $q$-exponentials

Tahara, Hidetoshi

doi:10.5802/aif.3124

q

-Analogues of Laplace and Borel transforms by means of

q

-exponentials [

q

-Analogues des transformées de Laplace et Borel au moyen de

q

-exponentielles ]

Tahara, Hidetoshi

Annales de l'Institut Fourier, Tome 67 (2017) no. 5, pp. 1865-1903.

Résumé
Abstract

Nous considérons certaines $q$ -analogues des transformées de Laplace et Borel et montrons une nouvelle formule d’inversion entre les transformées de $q$ -Laplace et de $q$ -Borel. Des $q$ -analogues des lemmes de type Watson et des opérateurs de convolution sont aussi discutés. Ces résultats donnent un nouveau cadre pour la sommabilité des séries formelles qui sont solutions d’équations aux $q$ -différences.

The article discusses certain $q$ -analogues of Laplace and Borel transforms, and shows a new inversion formula between $q$ -Laplace and $q$ -Borel transforms. $q$ -Analogues of Watson type lemma and convolution operators are also discussed. These results give a new framework of the summability of formal power series solutions of $q$ -difference equations.

Reçu le : 2015-01-22
Révisé le : 2016-12-04
Accepté le : 2016-12-07
Publié le : 2017-11-16

DOI : https://doi.org/10.5802/aif.3124
Classification : 44A10, 39A13, 40G10
Mots clés :

q

-analogue, transformation de

q

-Laplace, transformation de

q

-Borel, équation aux

q

-différence

@article{AIF_2017__67_5_1865_0,
     author = {Tahara, Hidetoshi},
     title = {$q$-Analogues of Laplace and Borel transforms by means of $q$-exponentials},
     journal = {Annales de l'Institut Fourier},
     pages = {1865--1903},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {67},
     number = {5},
     year = {2017},
     doi = {10.5802/aif.3124},
     language = {en},
     url = {archive.numdam.org/item/AIF_2017__67_5_1865_0/}
}

Tahara, Hidetoshi. $q$-Analogues of Laplace and Borel transforms by means of $q$-exponentials. Annales de l'Institut Fourier, Tome 67 (2017) no. 5, pp. 1865-1903. doi : 10.5802/aif.3124. http://archive.numdam.org/item/AIF_2017__67_5_1865_0/

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