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Journal of Function Spaces and Applications
Volume 2012, Article ID 405368, 14 pages
http://dx.doi.org/10.1155/2012/405368
Research Article

Note on Boehmians for Class of Optical Fresnel Wavelet Transforms

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), Selangor, 43400 Serdang, Malaysia

Received 4 July 2012; Accepted 27 August 2012

Academic Editor: Manuel Ruiz Galan

Copyright © 2012 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 extend the Fresnel-wavelet transform to the context of generalized functions, namely, Boehmians. At first, we study the Fresnel-wavelet transform in the sense of distributions of compact support. Based on this concept, we introduce two new spaces of Boehmians and proving certain related results. Further, we show that the extended transform establishes a linear and an isomorphic mapping between the Boehmian spaces. Moreover, conditions of continuity of the extended transform and its inverse with respect to δ and Δ convergence are discussed in some details.