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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.

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Deformation of the Heat Kernel and the Brownian Motion from the Perspective of the Ben Saïd–Kobayashi–ØRsted (k, a)-Generalized Laguerre Semigroup Theory

  • 会议论文

  • 发表日期：

    2026年

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  • Aoyama Temma

摘要

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.