Non-archimedean Pseudo-differential Operators $\mathscr{B}_{\psi_1,\psi_2}$ Connected with Fractional Fourier Transform


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Authors

  • Abhisekh Shekhar Department of Mathematics, C.M.Science College (A constituent unit of L.N.M.U., Darbhanga), Darbhanga, Bihar, India
  • Nawin Kumar Agrawal University Department of Mathematics, L. N. Mithila University, Darbhanga, Bihar, India

Keywords:

Non-archimedean analysis, Pseudo-differential operators, Fractional Fourier transform, dissipative operators, p-Adic analysis

Abstract

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 $L^{2}(\mathbb{Q}_{p})$.

Author Biography

Abhisekh Shekhar, Department of Mathematics, C.M.Science College (A constituent unit of L.N.M.U., Darbhanga), Darbhanga, Bihar, India

 

 

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Published

01-05-2023

How to Cite

Abhisekh Shekhar, & Nawin Kumar Agrawal. (2023). Non-archimedean Pseudo-differential Operators $\mathscr{B}_{\psi_1,\psi_2}$ Connected with Fractional Fourier Transform. International Journal of Mathematics And Its Applications, 11(2), 59–70. Retrieved from http://ijmaa.in/index.php/ijmaa/article/view/964

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Section

Research Article