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PreprintCC BY-NC-ND 4.0arXiv

Formal solution and strong asymptotic expansion of some initial value problem in two complex time variables, infinite order irregular singularities and Mahler transforms

  • Alberto Lastra
  • Stephane Malek
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Abstract

A formal solution to a partial differential equation of infinite order involving the action of Mahler-type operators in several variables is obtained. Such formal solutions is constructed by means of a fixed point argument applied to the integral representation of the deceleration operator in several variables that has been developed. The Laplace transform in two variables of the actual solution of a related problem in both Borel plane and Fourier space turns out to admit strong asymptotic expansion along adequate multidirections.

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Cite

BibTeXRIS
BibTeX
@misc{lastra2026formal,
  title = {{Formal solution and strong asymptotic expansion of some initial value problem in two complex time variables, infinite order irregular singularities and Mahler transforms}},
  author = {Alberto Lastra and Stephane Malek},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.12654},
  eprint = {2609.12654},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.12654},
  note = {CC BY-NC-ND 4.0},
}
RIS
TY  - UNPB
TI  - Formal solution and strong asymptotic expansion of some initial value problem in two complex time variables, infinite order irregular singularities and Mahler transforms
AU  - Alberto Lastra
AU  - Stephane Malek
PY  - 2026
DA  - 2026/09/11
PB  - arXiv
DO  - 10.48550/arxiv.2609.12654
UR  - https://arxiv.org/abs/2609.12654
AB  - A formal solution to a partial differential equation of infinite order involving the action of Mahler-type operators in several variables is obtained. Such formal solutions is constructed by means of a fixed point argument applied to the integral representation of the deceleration operator in several variables that has been developed. The Laplace transform in two variables of the actual solution of a related problem in both Borel plane and Fourier space turns out to admit strong asymptotic expansion along adequate multidirections.
ER  -