Journal of Pseudo-Differential Operators and Applications
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Linear canonical ripplet transform: theory and localization operators
Journal of Pseudo-Differential Operators and Applications - Tập 13 - Trang 1-24 - 2022
The ripplet transform is a refinement of the ordinary curvelet transform based on the non-parabolic scaling law for resolving two-dimensional singularities. However, the ripplet transform offers flexibility only in the angular window which is not feasible for optimizing the concentration of the ripplet spectrum. Therefore, there arises a fundamental question “whether it is possible to induce flexi......
Minimal and maximal extensions of M-hypoelliptic proper uniform pseudo-differential operators in $$L^p$$ -spaces on non-compact manifolds
Journal of Pseudo-Differential Operators and Applications - Tập 12 - Trang 1-22 - 2021
In the context of manifolds of bounded geometry, we show that the properties of proper uniform pseudo-differential operators (PUPDOs) constructed by Kordyukov, Meladze, and Shubin carry over to PUPDOs whose local representations have symbols belonging to the (weighted) class
$$M_{\rho ,\varLambda }^{m}$$
......
Mapping properties for the Bargmann transform on modulation spaces
Journal of Pseudo-Differential Operators and Applications - Tập 3 Số 1 - Trang 1-30 - 2012
On paracomposition and change of variables in paradifferential operators
Journal of Pseudo-Differential Operators and Applications - Tập 14 - Trang 1-50 - 2023
In this paper we revisit the hypothesis needed to define the “paracomposition” operator, an analogue to the classic pull-back operation in the low regularity setting, first introduced by Alinhac (Commun Part Differ Equ 11(1):87–121, 1986). More precisely we do so in two directions. First we drop the diffeomorphism hypothesis. Secondly we give estimates in global Sobolev and Zygmund spaces. Thus we......
Simultaneous triangularization of pseudo-differential systems
Journal of Pseudo-Differential Operators and Applications - Tập 4 - Trang 45-61 - 2013
Using generalized Sylvester equation, we first develop a scheme for triangularizing a pseudo-differential system and prove a necessary and sufficient condition for factorizing the system into lower and upper triangular systems (LU factorization) independent of lower order terms. We then investigate simultaneous triangularization of a pair of matrix valued pseudo-differential operators under certai......
The convergence constants and non linear approximations of fusion frames
Journal of Pseudo-Differential Operators and Applications - Tập 12 - Trang 1-13 - 2021
In this paper, we study the unconditional constant and nonlinear N-term approximation of fusion frames in Hilbert spaces. We show that the unconditional constant and greedy constant are bounded by a constant which is associated with the fusion frame bounds. We prove that the unconditional constant of cross fusion frame expansions satisfies the similar properties as long as the cross g-frame expans......
Windowed Bessel Fourier transform in quantum calculus and applications
Journal of Pseudo-Differential Operators and Applications - Tập 8 - Trang 723-749 - 2017
This paper deals firstly with some q-harmonic analysis properties for the q-windowed Bessel Fourier transform related to the q-Bessel function of the third kind as Plancherel formula, inversion formula in
$$\mathcal {L}_{q,2,\nu }$$
. Secondly, we......
Multilinear pseudo-differential operators on product of Local Hardy spaces with variable exponents
Journal of Pseudo-Differential Operators and Applications - Tập 10 - Trang 379-396 - 2018
In this paper, we establish a new atomic decomposition theory for Local Hardy spaces with variable exponents via local grand maximal characterization. By applying the refined atomic decomposition result, we prove that multilinear pseudo-differential operators are bounded on product of local Hardy spaces with variable exponents.
Windowed special affine Fourier transform
Journal of Pseudo-Differential Operators and Applications - Tập 11 Số 3 - Trang 1389-1420 - 2020
Boundedness and uniqueness of quaternion Weyl transform
Journal of Pseudo-Differential Operators and Applications - Tập 13 - Trang 1-24 - 2022
In this article, we prove that the quaternion Weyl transform (QWT) is a compact operator on
$$L^2({\mathbb {R}}^2,\mathbb Q)$$
for a certain class of symbols in
$$L^{r}\left( {\mathbb {R}}^{4},{\mathbb {Q}}\right) $$
......
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