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- W4287668834 abstract "This article describes a class of pseudo-differential operators begin{equation*} (mathcal{A}^{alpha}varphi)(x)=mathcal{F}^{-1}_{xi rightarrow x}left(left[max{|boldsymbol{psi}_{1}(||xi||_{p})|,|boldsymbol{psi}_{2}(||xi||_{p})|}right]^{-alpha}widehat{varphi}(xi)right), end{equation*} $varphiin mathcal{D}(mathbb{Q}_{p}^{n})$ and $alphainmathbb{C}$; here $left[max{|boldsymbol{psi}_{1}(||xi||_{p})|,|boldsymbol{psi}_{2}(||xi||_{p})|}right]^{-alpha}$ is the symbol of the operator $mathcal{A}^{alpha}$. These operators can be seen as a generalization of the Bessel potentials in the $p$-adic context. We show that the family $left(K_{alpha}right)_{alpha>0}$ of convolution kernels attached to generalized Bessel potentials $mathcal{A}^{alpha}$, $alpha>0$, determine a convolution semigroup on $mathbb{Q}_{p}^{n}$. Imposing certain conditions we have that $K_{alpha}$, $alpha>0$, is a probability measure on $mathbb{Q}_{p}^{n}$. Moreover, we will study certain properties corresponding to the Green function of the operator $mathcal{A}^{alpha}$ and we show that heat equations, naturally associated to these operators, describes the cooling (or loss of heat) in a given region over time." @default.
- W4287668834 created "2022-07-25" @default.
- W4287668834 creator A5053433383 @default.
- W4287668834 date "2020-09-11" @default.
- W4287668834 modified "2023-09-23" @default.
- W4287668834 title "Non-archimedean generalized Bessel potentials and their applications" @default.
- W4287668834 doi "https://doi.org/10.48550/arxiv.2009.05630" @default.
- W4287668834 hasPublicationYear "2020" @default.
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