Pseudo-differential operators associated with the fractional Hankel-Bessel transform
Fuente:
arXiv
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2026
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866908795395899392 |
|---|---|
| author | Pasawan, Durgesh |
| author_facet | Pasawan, Durgesh |
| contents | We introduce and study a new class of pseudo-differential operators associated with a fractional Hankel--Bessel transform. Motivated by the classical Hankel transform and the pseudo-differential operators associated with Bessel operators studied by Pathak and Pandey \cite{PathakPandey1995}, we define a fractional variant by inserting a fractional Fourier-type phase into the Hankel kernel. We then introduce global Shubin-type symbol classes adapted to this transform, derive kernel estimates and integral representations, and establish boundedness results on weighted L^{p}-spaces and on fractional Hankel--Sobolev spaces. This provides a new framework parallel to the classical Hankel pseudo-differential calculus, but in a fractional and global setting. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_03091 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Pseudo-differential operators associated with the fractional Hankel-Bessel transform Pasawan, Durgesh Functional Analysis 42C10, 42A38, 35S05, 46F12, 44A15 We introduce and study a new class of pseudo-differential operators associated with a fractional Hankel--Bessel transform. Motivated by the classical Hankel transform and the pseudo-differential operators associated with Bessel operators studied by Pathak and Pandey \cite{PathakPandey1995}, we define a fractional variant by inserting a fractional Fourier-type phase into the Hankel kernel. We then introduce global Shubin-type symbol classes adapted to this transform, derive kernel estimates and integral representations, and establish boundedness results on weighted L^{p}-spaces and on fractional Hankel--Sobolev spaces. This provides a new framework parallel to the classical Hankel pseudo-differential calculus, but in a fractional and global setting. |
| title | Pseudo-differential operators associated with the fractional Hankel-Bessel transform |
| topic | Functional Analysis 42C10, 42A38, 35S05, 46F12, 44A15 |
| url | https://arxiv.org/abs/2601.03091 |