A family of pseudo-differential operators on the Schwartz space associated with the fractional Fourier transform

Motivated essentially by their potential for applications in the mathematical, physical, and engineering sciences, the authors introduce and investigate various useful properties of a family of pseudo-differential operators on the Schwartz space S (ℝ) (i.e., the space of rapidly decreasing infinitel...

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Published inRussian journal of mathematical physics Vol. 24; no. 4; pp. 534 - 543
Main Authors Srivastava, H. M., Upadhyay, S. K., Khatterwani, K.
Format Journal Article
LanguageEnglish
Published Moscow Pleiades Publishing 01.10.2017
Springer Nature B.V
Subjects
Differential equations
Fourier transforms
Functions (mathematics)
Mathematical and Computational Physics
Operators (mathematics)
Physics
Physics and Astronomy
Theoretical
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ISSN1061-9208
1555-6638
DOI10.1134/S1061920817040124

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Summary:Motivated essentially by their potential for applications in the mathematical, physical, and engineering sciences, the authors introduce and investigate various useful properties of a family of pseudo-differential operators on the Schwartz space S (ℝ) (i.e., the space of rapidly decreasing infinitely differentiable functions on ℝ), which are associated with the fractional Fourier transform of order α (0 < α ≦ 1). Relevant connections with several related recent developments on this subject are also pointed out.
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ISSN:1061-9208
1555-6638
DOI:10.1134/S1061920817040124