Abstract and Applied Analysis
Volume 2011 (2011), Article ID 712746, 11 pages
http://dx.doi.org/10.1155/2011/712746
Research Article

On Diffraction Fresnel Transforms for Boehmians

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 12 September 2011; Revised 27 October 2011; Accepted 11 November 2011

Academic Editor: Natig Atakishiyev

Copyright © 2011 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

The theory of the diffraction Fresnel transform is extended to certain spaces of Schwartz distributions. In the context of Boehmian spaces, the diffraction Fresnel transform is obtained as a continuous function. Convergence with respect to 𝛿 and Δ is also defined.