The article discusses certain -analogues of Laplace and Borel transforms, and shows a new inversion formula between -Laplace and -Borel transforms. -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 -difference equations.
Nous considérons certaines -analogues des transformées de Laplace et Borel et montrons une nouvelle formule d’inversion entre les transformées de -Laplace et de -Borel. Des -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 -différences.
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Keywords: $q$-analogue, $q$-Laplace transform, $q$-Borel transform, $q$-difference equation
Mot clés : $q$-analogue, transformation de $q$-Laplace, transformation de $q$-Borel, équation aux $q$-différence
Tahara, Hidetoshi 1
@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{\textquoteright}institut Fourier}, volume = {67}, number = {5}, year = {2017}, doi = {10.5802/aif.3124}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.3124/} }
TY - JOUR AU - Tahara, Hidetoshi TI - $q$-Analogues of Laplace and Borel transforms by means of $q$-exponentials JO - Annales de l'Institut Fourier PY - 2017 SP - 1865 EP - 1903 VL - 67 IS - 5 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.3124/ DO - 10.5802/aif.3124 LA - en ID - AIF_2017__67_5_1865_0 ER -
%0 Journal Article %A Tahara, Hidetoshi %T $q$-Analogues of Laplace and Borel transforms by means of $q$-exponentials %J Annales de l'Institut Fourier %D 2017 %P 1865-1903 %V 67 %N 5 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.3124/ %R 10.5802/aif.3124 %G en %F 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, 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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