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arXiv · 2403.04658

Natural geometric Fourier transforms and the associated fractional Laplacian

Razvan M. Tudoran
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Abstract

To each arbitrary given general geometric structure on $\mathbb{R}^{n}$, we associate a pair of compatible Fourier transforms, that prove to appear naturally in the framework of Poisson's summation formula for full lattices. We study their properties and the compatibility with the classical $n-$dimensional Fourier transform. In the case of a positive definite geometric structure, we show that these geometric Fourier transforms induce a geometric fractional Laplacian, with properties similar to those of the classical fractional Laplacian.

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Razvan M. Tudoran. 2024-03-07. Natural geometric Fourier transforms and the associated fractional Laplacian. https://arxiv.org/abs/2403.04658

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