Boundedness of Pseudo-Differential Operator Associated with Fractional Fourier Transform

2014 ◽  
Vol 84 (4) ◽  
pp. 549-554 ◽  
Author(s):  
Akhilesh Prasad ◽  
Manish Kumar
Keyword(s):  
Fourier Transform ◽  
Differential Operator ◽  
Fractional Fourier Transform ◽  
Pseudo Differential Operator

scholarly journals Asymptotic Series of General Symbol of Pseudo-Differential Operator Involving Fractional Fourier Transform

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
S. K. Upadhyay ◽  
Anuj Kumar ◽  
Jitendra Kumar Dubey
Keyword(s):  
Fourier Transform ◽  
Differential Operator ◽  
Fractional Fourier Transform ◽  
Asymptotic Series ◽  
Pseudo Differential Operator

An asymptotic series of general symbol of pseudo-differential operator is obtained by using the theory of fractional Fourier transform.

A New Study of Shape and Size-dependent Properties of Nanocrystals Utilizing the Fractional Fourier Transform

2020 ◽  
Vol 5 (2) ◽  
pp. 165-174
Author(s):  
Aeshah Salem
Keyword(s):  
Fourier Transform ◽  
Infrared Spectroscopy ◽  
Fourier Transform Infrared Spectroscopy ◽  
Surface Area ◽  
Fractional Fourier Transform ◽  
Fourier Transform Infrared ◽  
Chemical Dynamics ◽  
Znse Nanoparticles ◽  
Size Dependent ◽  
Shape And Size

Background: Possessions of components, described by their shape and size (S&S), are certainly attractive and has formed the foundation of the developing field of nanoscience. Methods: Here, we study the S&S reliant on electronic construction and possession of nanocrystals by semiconductors and metals to explain this feature. We formerly considered the chemical dynamics of mineral nanocrystals that are arranged according to the S&S not only for the big surface area, but also as a consequence of the considerably diverse electronic construction of the nanocrystals. Results: The S&S of models, approved by using the Fractional Fourier Transform Infrared Spectroscopy (FFTIR), indicate the construction of CdSe and ZnSe nanoparticles. Conclusion: In order to study the historical behavior of the nanomaterial in terms of S&S and estimate further results, the FFTIR was used to solve this project.

The Mehler-Fock-Clifford transform and pseudo-differential operator on function spaces

Filomat ◽  
2019 ◽  
Vol 33 (8) ◽  
pp. 2457-2469
Author(s):  
Akhilesh Prasad ◽  
S.K. Verma
Keyword(s):  
Differential Operator ◽  
Function Spaces ◽  
Pseudo Differential Operator ◽  
Test Function ◽  
Basic Properties ◽  
Cone Function ◽  
Translation Operators

In this article, weintroduce a new index transform associated with the cone function Pi ??-1/2 (2?x), named as Mehler-Fock-Clifford transform and study its some basic properties. Convolution and translation operators are defined and obtained their estimates under Lp(I, x-1/2 dx) norm. The test function spaces G? and F? are introduced and discussed the continuity of the differential operator and MFC-transform on these spaces. Moreover, the pseudo-differential operator (p.d.o.) involving MFC-transform is defined and studied its continuity between G? and F?.

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