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arXiv · 2207.00359

Translation beyond Delsarte

Á. P. Horváth
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Abstract

We introduce general translations as solutions to Cauchy or Dirichlet problems. This point of view allows us to handle the heat-diffusion semigroup as a translation. With the given examples Kolmogorov-Riesz characterization of compact sets in certain $L^p_\mu$ spaces are given. Pego-type characterizations are also derived. Finally for some examples the equivalence of the corresponding modulus of smoothness and K-functional is pointed out.

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Á. P. Horváth. 2022-07-01. Translation beyond Delsarte. https://arxiv.org/abs/2207.00359

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