q-Analogues of Laplace and Borel transforms by means of q-exponentials
Annales de l'Institut Fourier, Volume 67 (2017) no. 5, pp. 1865-1903.

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.

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.

Published online:
DOI: 10.5802/aif.3124
Classification: 44A10, 39A13, 40G10
Keywords: $q$-analogue, $q$-Laplace transform, $q$-Borel transform, $q$-difference equation
Tahara, Hidetoshi 1

1 Sophia University Dept. of Information and Communication Sciences Kioicho, Chiyoda-ku, Tokyo 102-8554 (Japan)
License: CC-BY-ND 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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     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{\textquoteright}institut Fourier},
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Tahara, Hidetoshi. $q$-Analogues of Laplace and Borel transforms by means of $q$-exponentials. Annales de l'Institut Fourier, Volume 67 (2017) no. 5, pp. 1865-1903. doi : 10.5802/aif.3124. https://aif.centre-mersenne.org/articles/10.5802/aif.3124/

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