Deformation of the heat kernel and the Brownian motion from the perspective of the Ben Saïd--Kobayashi--Ørsted $(k,a)$-generalized Laguerre semigroup theory
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866909719714594816 |
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| author | Aoyama, Temma |
| author_facet | Aoyama, Temma |
| contents | We deform the heat kernel and the Brownian motion on $\mathbb{R}^{N}$ from the perspective of "$(k,a)$-generalized Fourier analysis" with $k=0$. This is a new type of harmonic analysis proposed by S.Ben Saïd--T.Kobayashi--B.Ørsted from the representation theoretic viewpoint. In this paper, we construct the $a$-deformed heat kernel and $a$-deformed Brownian motion, and explore their some basic properties. We also prove that the $(k,a)$-generalized Fourier integral kernels are polynomial growth when $k=0$, for a justification of some discussions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_03664 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Deformation of the heat kernel and the Brownian motion from the perspective of the Ben Saïd--Kobayashi--Ørsted $(k,a)$-generalized Laguerre semigroup theory Aoyama, Temma Representation Theory Analysis of PDEs Probability We deform the heat kernel and the Brownian motion on $\mathbb{R}^{N}$ from the perspective of "$(k,a)$-generalized Fourier analysis" with $k=0$. This is a new type of harmonic analysis proposed by S.Ben Saïd--T.Kobayashi--B.Ørsted from the representation theoretic viewpoint. In this paper, we construct the $a$-deformed heat kernel and $a$-deformed Brownian motion, and explore their some basic properties. We also prove that the $(k,a)$-generalized Fourier integral kernels are polynomial growth when $k=0$, for a justification of some discussions. |
| title | Deformation of the heat kernel and the Brownian motion from the perspective of the Ben Saïd--Kobayashi--Ørsted $(k,a)$-generalized Laguerre semigroup theory |
| topic | Representation Theory Analysis of PDEs Probability |
| url | https://arxiv.org/abs/2407.03664 |