## Fractional Fourier Transform on Sobolev Spaces Connected to Negative Definite Functions

Abhisekh Shekhar *

Department of Mathematics, C.M.Science College, Darbhanga-846004, (A Constituent Unit of L.N.M.U.), Darbhanga-846004) Bihar, India.

Nawin Kumar Agrawal

University Department of Mathematics, L. N. Mithila University Kameshwaranagar, Darbhanga, Bihar-846004, India.

*Author to whom correspondence should be addressed.

### Abstract

My objective is to define non-archimedean pseudo-differential operator associted with fractional Fourier transform in this manuscript. In this manuscript, we discuss some classes of \(\mathrm{p}\) -adic complete inner product spaces, \(\mathscr{B}_{\phi, k}\left(Q_p\right), \quad 0 \leq k<\infty\) , connected to negative definite, radial and continuous functions \(\phi: \mathbb{Q}_p \rightarrow \mathbb{C}\). In this article, we also introduce the non-archimedean pseudo-differential operator \(\mathscr{A}_{\phi k}\) involving fractional Fourier transform connected to negative definite functions. We| find the convolution Kernel \(\mathscr{K}_k\) of these operators and the Green function related to fractional Fourier transform.

Keywords: Non-archimedean analysis, Pseudo-differential operators, Fractional Fourier transform, M-dissipative operators

**How to Cite**

*Asian Journal of Pure and Applied Mathematics*,

*5*(1), 112–122. Retrieved from https://globalpresshub.com/index.php/AJPAM/article/view/1800

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