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Upadhyay, S. K.
- The Continuous Fractional Wavelet Transform on W-Type Spaces
Abstract Views :219 |
PDF Views:2
Authors
Anuj Kumar
1,
S. K. Upadhyay
2
Affiliations
1 Department of Mathematical Sciences, Indian Institute of Technology (Banaras Hindu University), Varanasi - 221005, IN
2 DST-CIMS, Department of Mathematical Sciences, Indian Institute of Technology (Banaras Hindu University), Varanasi - 221005, IN
1 Department of Mathematical Sciences, Indian Institute of Technology (Banaras Hindu University), Varanasi - 221005, IN
2 DST-CIMS, Department of Mathematical Sciences, Indian Institute of Technology (Banaras Hindu University), Varanasi - 221005, IN
Source
The Journal of the Indian Mathematical Society, Vol 85, No 3-4 (2018), Pagination: 377-395Abstract
An n-dimensional continuous fractional wavelet transform involving n-dimensional fractional Fourier transform is studied and its properties are obtained on Gel'fand and Shilov spaces of type WM(Rn), WΩ (Cn) and WΩM (Cn). It is shown that continuous fractional wavelet transform, WαψΦ : WM(Rn) → WM(Rn × R+), WαψΦ : WΩ (Cn) → WΩ (Cn × R+) and WαψΦ : WΩM (Cn) → WΩM (Cn × R+) are linear and continuous maps, where Rn and Cn are the usual Euclidean spaces.Keywords
Fractional Fourier Transform, Fractional Wavelet Transform, Convex Functions, Gel'fand and Shilov Spaces.
References
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- Pseudo-Differential Operators of Homogeneous Symbol Associated with n-Dimensional Hankel Transformation
Abstract Views :239 |
PDF Views:3
Authors
Affiliations
1 DST-CIMS and Department of Mathematics Science, IIT (BHU), Varanasi, IN
2 DST-CIMS, Institute of Science, Banaras Hindu University, Varanasi, IN
1 DST-CIMS and Department of Mathematics Science, IIT (BHU), Varanasi, IN
2 DST-CIMS, Institute of Science, Banaras Hindu University, Varanasi, IN
Source
The Journal of the Indian Mathematical Society, Vol 85, No 3-4 (2018), Pagination: 470-493Abstract
The characterizations of pseudo-differential operators L(x,D) and H(x,D) associated with the homogeneous symbol l(x; ξ), involving Hankel transformation are investigated by using the theory of n-dimensional Hankel transform.Keywords
Hankel Transform, Pseudo-Differential Operators, Sobolev Space.References
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- Characterization of Product of Pseudo-Differential Operators Involving Fractional Fourier Transform
Abstract Views :186 |
PDF Views:0
Authors
Affiliations
1 Department of Mathematics, Galgotias University, Greater Noida, 226001, IN
2 Department of Mathematics, DCSK P. G. College, Mau - 275101, IN
3 Department of Mathematical Sciences, Indian Institute of Technology (BHU), Varanasi - 221005, IN
1 Department of Mathematics, Galgotias University, Greater Noida, 226001, IN
2 Department of Mathematics, DCSK P. G. College, Mau - 275101, IN
3 Department of Mathematical Sciences, Indian Institute of Technology (BHU), Varanasi - 221005, IN
Source
The Journal of the Indian Mathematical Society, Vol 88, No 1-2 (2021), Pagination: 60–71Abstract
Characterizations of product of generalized pseudo-differential operators associated with symbol σ(x,ξ) ∈ Sm are discussed by exploiting the fractional Fourier transform.Keywords
Fractional Fourier transform, Pseudo-differential operator, Adjoint operatorReferences
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- J. K. Dubey, A. Kumar and S. K. Upadhyay, Pseudo-differential operators and Localization operators on Sμv (R) space involving fractional Fourier transform, Novi Sad J. Math., 45(2015), 285–301.
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- S. K. Upadhyay and J. K. Dubey, Pseudo-Differential Operators of infinite order on WΩM (Cn)- spaces involving fractional Fourier transform, J. Pseudo-Differ. Oper. Appl. 6 (2015), 113–133.
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