Pseudo-Differential Operators Associated to a Pair of Hankel–clifford Transformations on Certain Beurling Type Function Spaces

Abstract

A brief introduction to the Hankel–Clifford transformations and its basic properties is given. The spaces [Formula: see text] and [Formula: see text] generalizing the spaces Hμ(I) and S(I), respectively are defined. It is given that the pseudo-differential operators h1,μ,a and h2,μ,a are automorphism of [Formula: see text] and [Formula: see text], respectively. Product and convolution on [Formula: see text] and [Formula: see text] are investigated. Some other spaces related to [Formula: see text] and [Formula: see text] are introduced and studied the continuity of the pseudo-differential operators h1,μ,a and h2,μ,a, respectively.

The Mehler-Fock-Clifford transform and pseudo-differential operator on function spaces

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“…The theory and properties of Hankel-Clifford transform have already been studied by the several researchers viz [12,14,15] etc. As per this argument the Legendre-Clifford function according to [1, p.156] is defined as…”

Two versions of pseudo-differential operators involving the Kontorovich–Lebedev transform in L 2(ℝ+;dx/x)

“…Some pseudo-differential operators associated with other integral transformations like Hankel transformations, Fourier-Jacobi transformations etc. are defined and their properties are discussed in [13,15,16,21]. Motivated by the works of Zaidman [31] and Pathak and Upadhyay [15], we define the pseudo-differential operator…”

The Kontorovich‐Lebedev transform and its associated pseudodifferential operator

“…associated with various integral transformations on various function spaces, we refer to references herein. ()…”