On the Generalized Krätzel Transform and Its Extension to Bohemian Spaces

S K Q Al-Omari,Adem Kılıçman

doi:10.1155/2013/841585

S K Q Al-Omari, Adem Kılıçman

Open Access

https://doi.org/10.1155/2013/841585

Copy DOI

Abstract

We investigate the Krätzel transform on certain class of generalized functions. We propose operations that lead to the construction of desired spaces of generalized functions. The Krätzel transform is extended and some of its properties are obtained.

Highlights

In recent years, integral transforms of Bohemian have comprised an active area of research
We investigate the Kratzel transform on certain class of generalized functions
We propose operations that lead to the construction of desired spaces of generalized functions

Summary

Introduction

Integral transforms of Bohemian have comprised an active area of research. Several integral transforms are extended to various spaces of Bohemian, especially, that permit a factorization property of Fourier convolution type. Several integral transforms that have not permitted a factorization property of Fourier convolution type are extended to various spaces of Bohemian. Ρ > 0 (∈ N), V ∈ C, x > 0 is extended to certain space S+(lr, of α, ultra-Bohemian, denoted by S+ {αi}, a), 1 ≤ r ≤ ∞, respectively. Due to [3, Proposition 2.1], we state the following theorem. By D(R+), or D, denote the Schwartz space of test functions of compact support defined on R+. By (9), we have lV(ρ) (f ⋎ φ) (x) = ((lV(ρ)f) ⊗ φ) (x)

General Bohemian

Krätzel Transform of Bohemian