Note on Boehmians for Class of Optical Fresnel Wavelet Transforms

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....

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Bibliographic Details
Published in:Journal of function spaces Vol. 2012; no. 2012; pp. 1 - 14
Main Authors: al-Omari, S. K. Q., Kiliçman, Adem
Format: Journal Article
Language:English
Published: Cairo, Egypt Hindawi Puplishing Corporation 01.01.2012
Hindawi Publishing Corporation
John Wiley & Sons, Inc
Wiley
Subjects:
Continuity
Convergence
Deltas
Fourier transforms
Function space
Inverse
Mapping
Optics
Studies
Transforms
Wavelet transforms
ISSN:0972-6802, 2314-8896, 1758-4965, 2314-8888
Online Access:Get full text
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Summary: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.
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ISSN:0972-6802
2314-8896
1758-4965
2314-8888
DOI:10.1155/2012/405368