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Pseudo-differential operator associated with the fractional Fourier transform.

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Title: Pseudo-differential operator associated with the fractional Fourier transform.
Authors: PRASAD, AKHILESH1 apr_bhu@yahoo.com, KUMAR, PRAVEEN1 praveen502mzn@gmail.com
Source: Mathematical Communications. 2016, Vol. 21 Issue 1, p115-126. 12p.
Subjects: Pseudocode (Computer program language), Fourier transforms, Schwartz spaces, Cepstrum analysis (Mechanics), Fourier analysis
Abstract: The main goal of this paper is to study properties of the fractional Fourier transform on Schwartz type space ℒθ. Symbol class Sρ,σm,θ is introduced. The fractional pseudo-differential operators (f.p.d.o.) associated with the symbol a(x, ξ) are a continuous linear mapping of ℒ into ℒθ. Kernel and integral representations of f.p.d.o are obtained. The boundedness property of f.p.d.o. is studied. Application of the fractional Fourier transform in solving a generalized Fredholm integral equation is also given. [ABSTRACT FROM AUTHOR]
Copyright of Mathematical Communications is the property of University of Osijek, Department of Mathematics and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: Pseudo-differential operator associated with the fractional Fourier transform.
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  Data: <searchLink fieldCode="AR" term="%22PRASAD%2C+AKHILESH%22">PRASAD, AKHILESH</searchLink><relatesTo>1</relatesTo><i> apr_bhu@yahoo.com</i><br /><searchLink fieldCode="AR" term="%22KUMAR%2C+PRAVEEN%22">KUMAR, PRAVEEN</searchLink><relatesTo>1</relatesTo><i> praveen502mzn@gmail.com</i>
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  Data: <searchLink fieldCode="JN" term="%22Mathematical+Communications%22">Mathematical Communications</searchLink>. 2016, Vol. 21 Issue 1, p115-126. 12p.
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  Data: <searchLink fieldCode="DE" term="%22Pseudocode+%28Computer+program+language%29%22">Pseudocode (Computer program language)</searchLink><br /><searchLink fieldCode="DE" term="%22Fourier+transforms%22">Fourier transforms</searchLink><br /><searchLink fieldCode="DE" term="%22Schwartz+spaces%22">Schwartz spaces</searchLink><br /><searchLink fieldCode="DE" term="%22Cepstrum+analysis+%28Mechanics%29%22">Cepstrum analysis (Mechanics)</searchLink><br /><searchLink fieldCode="DE" term="%22Fourier+analysis%22">Fourier analysis</searchLink>
– Name: Abstract
  Label: Abstract
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  Data: The main goal of this paper is to study properties of the fractional Fourier transform on Schwartz type space ℒθ. Symbol class Sρ,σm,θ is introduced. The fractional pseudo-differential operators (f.p.d.o.) associated with the symbol a(x, ξ) are a continuous linear mapping of ℒ into ℒθ. Kernel and integral representations of f.p.d.o are obtained. The boundedness property of f.p.d.o. is studied. Application of the fractional Fourier transform in solving a generalized Fredholm integral equation is also given. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Mathematical Communications is the property of University of Osijek, Department of Mathematics and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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      – Code: eng
        Text: English
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        PageCount: 12
        StartPage: 115
    Subjects:
      – SubjectFull: Pseudocode (Computer program language)
        Type: general
      – SubjectFull: Fourier transforms
        Type: general
      – SubjectFull: Schwartz spaces
        Type: general
      – SubjectFull: Cepstrum analysis (Mechanics)
        Type: general
      – SubjectFull: Fourier analysis
        Type: general
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      – TitleFull: Pseudo-differential operator associated with the fractional Fourier transform.
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            NameFull: PRASAD, AKHILESH
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            NameFull: KUMAR, PRAVEEN
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              Text: 2016
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