Abstract and Applied Analysis
Volume 2013 (2013), Article ID 750524, 7 pages
http://dx.doi.org/10.1155/2013/750524
Research Article

Unified Treatment of the Krätzel Transformation for Generalized Functions

S. K. Q. Al-Omari1 and A. Kılıçman2

1Department of Applied Sciences, Faculty of Engineering Technology, Al-Balqa Applied University, Amman 11134, Jordan
2Department of Mathematics and Institute of Mathematical Research, Universiti Putra Malaysia (UPM), 43400 Serdang, Selangor, Malaysia

Received 26 March 2013; Accepted 18 April 2013

Academic Editor: Mustafa Bayram

Copyright © 2013 S. K. Q. Al-Omari and A. Kılıçman. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We discuss a generalization of the Krätzel transforms on certain spaces of ultradistributions. We have proved that the Krätzel transform of an ultradifferentiable function is an ultradifferentiable function and satisfies its Parseval's inequality. We also provide a complete reading of the transform constructing two desired spaces of Boehmians. Some other properties of convergence and continuity conditions and its inverse are also discussed in some detail.