Non-archimedean Pseudo-differential Operators $\mathscr{B}_{\psi_1,\psi_2}$ Connected with Fractional Fourier Transform
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Keywords:
Non-archimedean analysis, Pseudo-differential operators, Fractional Fourier transform, dissipative operators, p-Adic analysisAbstract
The aim of this paper is to introduce non-archimedean pseudo-differential operators $\mathscr{B}_{\psi_1,\psi_2}$ connected with fractional Fourier transform whose symbol $\text{min}\{|\psi_1(.)|,|\psi_2(.)|\}$ is found from the character of two mappings defined on the p-adic numbers. In this manuscript, we also study some properties of fractional heat Kernel $\mathscr{Z}(\zeta,\tau)$ on $\mathbb{Q}_{p}$, self-adjoint of $\mathscr{B}_{\psi_1,\psi_2}$ and dissipative of $\mathscr{B}_{\psi_1,\psi_2}$ in $L^{2}(\mathbb{Q}_{p})$.
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