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| Auteur principal: | |
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| Format: | Preprint |
| Publié: |
2024
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| Sujets: | |
| Accès en ligne: | https://arxiv.org/abs/2407.03664 |
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Table des matières:
- 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.