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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Vydáno v:Journal of function spaces Ročník 2012; číslo 2012; s. 1 - 14
Hlavní autoři: al-Omari, S. K. Q., Kiliçman, Adem
Médium: Journal Article
Jazyk:angličtina
Vydáno: Cairo, Egypt Hindawi Puplishing Corporation 01.01.2012
Hindawi Publishing Corporation
John Wiley & Sons, Inc
Wiley
Témata:
Continuity
Convergence
Deltas
Fourier transforms
Function space
Inverse
Mapping
Optics
Studies
Transforms
Wavelet transforms
ISSN:0972-6802, 2314-8896, 1758-4965, 2314-8888
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Shrnutí: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