Linear Canonical Transforms on the Zemanian Spaces

1
Dr. A S Gudadhe
Dr. A S Gudadhe
1 Govt. Vidarbha Institute of Science and Humanities,

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GJSFR Volume 12 Issue F8

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Linear Canonical Transforms on the Zemanian Spaces Banner
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The objective of this paper is to make the theory of Linear canonical transform mathematically rigorous. Here we define the linear canonical transform on the Zemanian space 𝓢𝓢𝓢𝓢, the space of functions of rapid descent, and prove some results. We have also discussed some operation formulae for linear canonical transform on this space.

6 Cites in Articles

References

  1. O Akay,G Boudreaux-Bartels (1998). Unitary and Hermitian fractional operators and their relation to the fractional Fourier transform.
  2. L Almeida (1997). Product and Convolution Theorems for the Fractional Fourier Transform.
  3. A S Gudadhe,P P ; Thakare,Kerr (1988). F H: A distributional approach to Namias Fractional Fourier transform.
  4. V Namias (1980). The Fractional Fourier Transform and Its application in Quantum Mechanics.
  5. H Ozaktas,Z Zalevsky,M Kutay (2001). The Fractional Fourier Transform with Applications in Optics and Signal Proessing.
  6. A Zemanian (1965). Distribution Theory and Transform Analysis.

Funding

No external funding was declared for this work.

Conflict of Interest

The authors declare no conflict of interest.

Ethical Approval

No ethics committee approval was required for this article type.

Data Availability

Not applicable for this article.

Dr. A S Gudadhe. 2012. \u201cLinear Canonical Transforms on the Zemanian Spaces\u201d. Global Journal of Science Frontier Research - F: Mathematics & Decision GJSFR-F Volume 12 (GJSFR Volume 12 Issue F8): .

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Issue Cover
GJSFR Volume 12 Issue F8
Pg. 17- 23
Journal Specifications

Crossref Journal DOI 10.17406/GJSFR

Print ISSN 0975-5896

e-ISSN 2249-4626

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v1.2

Issue date

July 27, 2012

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English

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The objective of this paper is to make the theory of Linear canonical transform mathematically rigorous. Here we define the linear canonical transform on the Zemanian space 𝓢𝓢𝓢𝓢, the space of functions of rapid descent, and prove some results. We have also discussed some operation formulae for linear canonical transform on this space.

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Linear Canonical Transforms on the Zemanian Spaces

Dr. A S Gudadhe
Dr. A S Gudadhe Govt. Vidarbha Institute of Science and Humanities,

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