SOME NEW APPLICATIONS OF LAPLACE-WEIERSTRASS TRANSFORM

This paper is devoted to some new applications of Laplace-Weierstrass transform (i.e., for solving two dimensional diffusion equations). Solution of Cauchy’s linear differential equation is also given. Some results are also given which are required for solving Cauchy’s linear differential equation.

Convergence and Inversion Theorems for Generalized Weierstrass Transform

In this paper , we study the Weierstrass Transformation of certain generalized functions and their convolution transformation of certain generalised function and its inversion . We extend such type of results of convergence and inversion theorems for generalized weierstrass transforms (1.1) and (1.2).

Sobolev-Type Spaces on the Dual of the Chébli-Trimèche Hypergroup and Applications

We define and study Sobolev-type spacesWAs,pℝ+associated with singular second-order differential operator on0,∞. Some properties are given; in particular we establish a compactness-type imbedding result which allows a Reillich-type theorem. Next, we introduce a generalized Weierstrass transform and, using the theory of reproducing kernels, some applications are given.

Best approximations for the Laguerre-type Weierstrass transform on[0,∞[×ℝ

We use reproducing kernel Hilbert spaces to give the best approximation for Laguerre-type Weierstrass transform. Estimates of extremal functions are also discussed.