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Lie Groups and Representation Theory
Seminar information archive ～04/28｜Next seminar｜Future seminars 04/29～
| Date, time & place | Tuesday 16:30 - 18:00 126Room #126 (Graduate School of Math. Sci. Bldg.) |
|---|
2023/05/16
17:00-18:00 Room #online (Graduate School of Math. Sci. Bldg.)
Hiroyoshi TAMORI (Shibaura institute of technology)
Integral expression of the $(k,a)$-generalized Laguerre semigroup
(Japanese)
Hiroyoshi TAMORI (Shibaura institute of technology)
Integral expression of the $(k,a)$-generalized Laguerre semigroup
(Japanese)
[ Abstract ]
The $(k,a)$-generalized Laguerre semigroup was introduced by Ben
Sa\"{\i}d--Kobayashi-{\O}rsted as an interpolation of the Hermite semigroup (the k=0, a=2 case) and the Laguerre semigroup (the k=0, a=1 case). Based on a joint work with Kouichi Taira (Ritsumeikan University), I will explain an integral expression of the semigroup and an upper estimate of the integral kernel, which leads to Strichartz estimates for operators $|x|^{2-a}\Delta_{k}-|x|^a$ and $|x|^{2-a}\Delta_{k}$ ($\Delta_k$ denotes the Dunkl Laplacian) under some condition on the deformation parameter $(k,a)$.
The $(k,a)$-generalized Laguerre semigroup was introduced by Ben
Sa\"{\i}d--Kobayashi-{\O}rsted as an interpolation of the Hermite semigroup (the k=0, a=2 case) and the Laguerre semigroup (the k=0, a=1 case). Based on a joint work with Kouichi Taira (Ritsumeikan University), I will explain an integral expression of the semigroup and an upper estimate of the integral kernel, which leads to Strichartz estimates for operators $|x|^{2-a}\Delta_{k}-|x|^a$ and $|x|^{2-a}\Delta_{k}$ ($\Delta_k$ denotes the Dunkl Laplacian) under some condition on the deformation parameter $(k,a)$.
