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q-middle Laplace transform and its applications
Abstract
We introduce a q-analog of the one-variable middle Laplace transform defined by the first author. We establish its invertibility and preservation of irreducibility, and derive a decomposition of q-middle convolution in terms of this transform. As applications, we obtain integral representations of solutions to the confluent q-hypergeometric equation and its variant, and construct a transformation of the 2× 2 Lax linear equation associated with the q-Painlevé equation of type A4(1).
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BibTeX
@misc{adachi2026qmiddle,
title = {{$q$-middle Laplace transform and its applications}},
author = {Shunya Adachi and Takahiko Nobukawa},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.29490},
eprint = {2610.29490},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.29490},
}
RIS
TY - UNPB
TI - q-middle Laplace transform and its applications
AU - Shunya Adachi
AU - Takahiko Nobukawa
PY - 2026
DA - 2026/10/21
PB - arXiv
DO - 10.48550/arxiv.2610.29490
UR - https://arxiv.org/abs/2610.29490
AB - We introduce a q-analog of the one-variable middle Laplace transform defined by the first author. We establish its invertibility and preservation of irreducibility, and derive a decomposition of q-middle convolution in terms of this transform. As applications, we obtain integral representations of solutions to the confluent q-hypergeometric equation and its variant, and construct a transformation of the 2× 2 Lax linear equation associated with the q-Painlevé equation of type A_4^(1).
ER -