SOLUTION OF INTEGRAL EQUATIONS BY BESSEL WAVELET TRANSFORM

The integral equations of the first kind arise in many areas of science and engineering fields such as image processing and electromagnetic theory. The wavelet transform technique to solve integral equation allows the creation of very fast algorithms when compared with known algorithms. Various wavelet methods are used to solve certain type of integral equations. To find the most accurate and stable solution of the integral equation Bessel wavelet is the appropriate method. To study the properties of solution of integral equations on distribution spaces Bessel wavelet transform is also used. In this paper, we accomplished the concept of Hankel convolution and continuous Bessel wavelet transform to solve certain types of integral equations (Volterra integral equation of first kind, Volterra integral equation of second kind and Abel integral equation). Also distributional wavelet transform and generalized convolution will be applied to find the solution of certain Integral equations.

The relation between Bessel wavelet convolution product and Hankel convolution product involving Hankel transform

In this paper, the relation between Bessel wavelet convolution product and Hankel convolution product is obtained by using the Bessel wavelet transform and the Hankel transform. Approximation results of the Bessel wavelet convolution product are investigated by exploiting the Hankel transformation tool. Motivated from the results of Pinsky, heuristic treatment of the Bessel wavelet transform is introduced and other properties of the Bessel wavelet transform are studied.

Integrability of the continuum Bessel wavelet kernel

In this paper, the sufficient condition for the integrability of the kernel of the inverse Bessel wavelet transform is obtained by using the theory of Hankel transform and Hankel convolution.

PSEUDO-DIFFERENTIAL OPERATORS INVOLVING HANKEL–CLIFFORD TRANSFORMATION

Pseudo-differential operator (p.d.o) associated with the symbol a(x, y) whose derivatives satisfy certain growth condition is defined and the Zemanian-type spaces Hμ(I) and S(I) are introduced. It is shown that the p.d.o is continuous linear map of the space Hμ(I) and S(I) into itself. An integral representation of p.d.o h1, μ, a is obtained. Using the Hankel convolution it is shown that p.d.o h1, μ, a satisfies a certain [Formula: see text]-norm inequality. Properties of Sobolev-type space [Formula: see text] are studied.

Calderón's reproducing formula for Hankel convolution

Calderón-type reproducing formula for Hankel convolution is established using the theory of Hankel transform.

Hankel Convolution Operators on Spaces of Entire Functions of Finite Order

In this paper we study Hankel transforms and Hankel convolution operators on spaces of entire functions of finite order and their duals.

On the surjectivity of Hankel convolution operators on Beurling-type distribution spaces

In this paper we consider Beurling-type distributions in the Hankel setting. The Hankel transform and Hankel convolution are studied on Beurling-type distributions. We also introduce a class of ultra-differential operators that allows us to show a Hankel version of the second structure theorem of Komatsu and Braun. Necessary and sufficient conditions are established in order that a Beurling distribution generates a surjective Hankel convolution operator.

On the surjectivity of Hankel convolution operators on Beurling-type distribution spaces

In this paper we consider Beurling-type distributions in the Hankel setting. The Hankel transform and Hankel convolution are studied on Beurling-type distributions. We also introduce a class of ultra-differential operators that allows us to show a Hankel version of the second structure theorem of Komatsu and Braun. Necessary and sufficient conditions are established in order that a Beurling distribution generates a surjective Hankel convolution operator.