Some Results on Pseudo-differential Operators Related Coupled Fractional Fourier Transform Involving Semi-norms & Norms
Abhisekh Shekhar *
Department of Mathematics, C.M.Science College, Darbhanga-846004, Bihar, India.
*Author to whom correspondence should be addressed.
Abstract
In this manuscript, some results on the Pseudo-differential operators (p.d.o.) L(x, y,D′ x,y) and L(x, y,D′ x,y) are found by using semi-norms and norms in Herbitian Spaces, a set of compact operators and L2(R×R) with the symbol classes Λ(R × R × R × R). In this paper, we also introduce the characterization of norms of the coupled fractional Fourier transform (CFrFT). Few mathematical properties on norms of pseudo-differential operators (P.D.O) connected with CFrFT are investigated. We conclude the manuscript by applying some of axioms to obtain the proofs of the Lemma and Theorems.
Keywords: Coupled fractional fourier transform, symbol classes, pseudo-differential operators