Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2509.06146 |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866909775516663808 |
|---|---|
| author | Lastra, Alberto Malek, Stephane |
| author_facet | Lastra, Alberto Malek, Stephane |
| contents | A family of $q$-difference-differential equations in two complex variables is studied, under the action of a so-called Mahler transform on time variable. The appearance of a leading formal $q$-difference operator of irregular type in the equation guarantees the existence of a formal solution to the main problem in time variable, which turns out to be obtained after a $q$-analog of Borel-Laplace procedure. Such formal solution to the main problem is $G_q$-summable along certain directions. The $G_q$-sums of such formal solutions do not in general satisfy the initial problem but rather turns out to be the analytic solutions to some related pseudo $q$-difference-differential equation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_06146 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On some $q$-analog of an initial value problem with infinite order irregular singularity and Mahler transforms Lastra, Alberto Malek, Stephane Complex Variables A family of $q$-difference-differential equations in two complex variables is studied, under the action of a so-called Mahler transform on time variable. The appearance of a leading formal $q$-difference operator of irregular type in the equation guarantees the existence of a formal solution to the main problem in time variable, which turns out to be obtained after a $q$-analog of Borel-Laplace procedure. Such formal solution to the main problem is $G_q$-summable along certain directions. The $G_q$-sums of such formal solutions do not in general satisfy the initial problem but rather turns out to be the analytic solutions to some related pseudo $q$-difference-differential equation. |
| title | On some $q$-analog of an initial value problem with infinite order irregular singularity and Mahler transforms |
| topic | Complex Variables |
| url | https://arxiv.org/abs/2509.06146 |