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In this article, we present some boundedness results of fractional Hankel transform on Gelfand–Shilov spaces of type S. Certain inequalities are obtained for pseudo-differential operators involving the fractional Hankel transform on Gelfand–Shilov spaces of type S. This article made further discussion on the continuity properties of fractional Hankel transform and pseudo-differential operator on some ultradifferentiable function spaces. [ABSTRACT FROM AUTHOR]

In this work we introduce and study a class of linear operators related to a finite measure space, for which its L 2 -Hilbert space is separable. These linear operators represent a generalization of pseudo-differential operators on S 1 , where S 1 is the unit circle with centre at the origin. We call these operators, S-operators or generalized pseudo-differential operators on S, where (S , B , m) is the corresponding finite measure space for which the L 2 -space is separable. We give some L 2 -boundedness and compactness results, and we also study the Hilbert–Schmidt property in connection with this class of linear operators. In the end we give some examples of finite measure spaces and corresponding S-operators for which we can apply our results. [ABSTRACT FROM AUTHOR]

In this work, we have introduced a pair of linear canonical Hankel transformations and investigated some of its properties on Zemanian-type spaces. Moreover two versions of pseudo-differential operator associated with canonical Hankel transformations are defined and discussed its integral representation. [ABSTRACT FROM AUTHOR]

In this paper we find a formula for the adjoint of bounded pseudo-differential operators on compact Lie groups, which yields a necessary and sufficient condition for self-adjointness of these operators. By a similar method we find necessary and sufficient conditions for bounded pseudo-differential operators on compact Lie groups to be normal or unitary and we give some examples of our results on . Then we show that similar results are true for some bounded pseudo-differential operators on . [ABSTRACT FROM AUTHOR]

The main aim of this paper is to find out the estimates of convolution for zero-order Mehler–Fock transform with various approaches. Pseudo-differential operator in terms of zero-order Mehler–Fock transform is defined and obtained its another integral representation. Further, its estimate in Lebesgue space has been studied. At the end some applications of zero-order Mehler–Fock transform and of convolution are discussed. [ABSTRACT FROM PUBLISHER]

A pair of pseudo-differential operators (p.d.o.) involving the Kontorovich–Lebedev transform (KL-transform) as well as its adjoint is defined. Estimates for translation and convolution function associated with the Kontorovich–Lebedev transform are obtained. Continuity of KL-transform and p.d.o. onandare discussed. [ABSTRACT FROM AUTHOR]

The pseudo-differential operator involving the Kontorovich–Lebedev transform is defined. The boundedness of pseudo differential operator in a certain Sobolev-type space is shown. Composition of pseudo-differential operatorsis defined in terms of the two symbols, and also its boundedness in certain Sobolev-type space is given. Some special cases are also discussed. Finally, the Kontorovich–Lebedev transform is used in the solution of some partial differential equations. [ABSTRACT FROM PUBLISHER]

A class of pseudo-differential operators (p.d.o.'s) associated with the general Fourier kernel studied by Hardy and Titchmarsh is defined. A symbol class Tm is introduced. It is shown that the p.d.o.'s associated with the symbol are continuous linear mappings of the Braaksma and Schuitman space T(λ,μ) into itself. An integral representation of p.d.o. is obtained. Some special forms of the symbol are considered. It is shown that these p.d.o.'s and their products are bounded in certain Sobolev type space. [ABSTRACT FROM AUTHOR]

L p -norm type inequalities for pseudo-differential operators L ( x,D ) and H ( x,D ) are derived for 1 ≤ p < ∞. Product of pseudo-differential operators associated with Bessel operator S μ are defined and its L p -norm type inequalities are obtained. [ABSTRACT FROM AUTHOR]

Using Hankel transform the symbol ' a ' is defined and the pseudo-differential operator (p.d.o.) h μ, a associated with the Bessel operator d 2 / dx 2 + (1 - 4μ 2 ) / 4 x 2 in terms of this symbol is defined. It is shown that the operator h μ, a is a continuous linear map of a Hankel invariant space into itself. A special pseudo-differential operator called the Hankel potential is defined and some of its properties are investigated. [ABSTRACT FROM AUTHOR]