Boundedness and compactness of localization operators for Weinstein–Wigner transform

Saoudi, A.; Nefzi, Bochra

doi:10.1007/s11868-020-00328-0

Cited by 21 publications

(13 citation statements)

References 25 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The Weinstein transform has rich calculus and nice mathematical background contains applications in Wavelets, Quantum calculus and other areas of Mathematical sciences. Utilising the theory of The Weinstein transform, the continuous Weinstein Wavelet transform was developed by authors [22], [11], [14], [6], [24], and found useful results. Exploiting the theory of the Weinstein convolution on ultradistributions, authors discussed various properties of the Weinstein transform on the spaces of types D ω , D ′ ω , E ω and S ω and obtained many observations.…”

Section: Discussionmentioning

confidence: 99%

The Weinstein transform associated with generalized distributions

Upadhyay

Yadav

2022

Preprint

View full text Add to dashboard Cite

Björck [4], and Hörmander [8], investigated the linear partial differential operators and generalized distributions associated with the Fourier transform by utilizing the convolution properties on the spaces of types Dω(Rn), Eω(Rn), and Sω(Rn). Motivated by above results the present paper examined various properties of the Wein-stein transform over generalized distributions Dω (R+n+1) and other spaces. The convolution properties of generalized distributions associated with the Weinstein transform on space Dω (R+n+1) ) are discussed. Mathematics Subject Classification (2010). 46F05. 46F10. 46F12. 42A85.

show abstract

Section: Discussionmentioning

confidence: 99%

The Weinstein transform associated with generalized distributions

Upadhyay

Yadav

2022

Preprint

View full text Add to dashboard Cite

show abstract

“…The theory of localization operators associated with the Fourier-Wigner transform has been studied and known remarkable development in many settings for example in the Riemann-Liouville setting [11],in the spherical mean setting [12],in the Laguerre setting [13],in the Dunkl setting [14],in the Weinstein setting [17],in the Heckman-Opdam-Jacobi setting [1],so its natural to ask whether there exists the equivalent of the theory of localization operators in other setting as the Laguerre Bessel setting. Following Wong's point of view,our main aim in this paper is to prove the analogues of the results on the localization operators studies by the authors in [1], [11], [12], [13], [14], [17] in the Laguerre-Bessel frame.…”

Section: Introductionmentioning

confidence: 99%

Spectral theorems for Wigner transform associated with the Laguerre-Bessel localization operators

Chana¹,

Akhlidj²

2023

Preprint

View full text Add to dashboard Cite

The main crux of this work is to study the Wigner transform associated with the Laguerre-Bessel operator and to give some results related to this transform. Next motivated by Wong's point of view we define a class of pseudo-differential operator Lu,v (σ) called localization operator wich depend on a symbol σ and two functions u and v, we give a criteria in terms of the symbol σ for its boundedness and compactness, we also show that these operators belongs to the Schatten-Von Neumann class S p for all p ∈ [1; + ∞] and we give a trace formula. MSC2020-Mathematics Subject Classification: 42B10, 47G30, 47B10.

show abstract

“…is the Bessel operator. (see [3], [4], [5] and [19]). For all f ∈ L 1 (R d+1 + , dµ α,d (x)), we define the Weinstein transform F α,d,n W by:…”

Section: Introductionmentioning

confidence: 99%

Extremal Functions on Generalized Weinstein Sobolev-gevrey spaces

Chaffar¹,

Mohamed²

2022

Preprint

View full text Add to dashboard Cite

Note: Please see pdf for full abstract with equations. The Weinstein operator $\Delta_{W}^{\alpha,d}$, mostly referred to as theLaplace-Bessel differential operator is now known as an important operator inanalysis, because of its applications in pure and applied Mathematics,especially in Fluid Mechanics. In this paper, we consider the generalizedWeinstein operator $\Delta_{W}^{d,\alpha,n}$, we introduce and study theSobolev-Gevrey spaces associated with the generalized Weinstein operator andinvestigate their properties. Next, as application, we study the extremalfunctions on the spaces $\mathscr H_{a,\sigma}^{s,\alpha,n}(\mathbb{R}%_{+}^{d+1})$ using the theory of reproducing kernels. Mathematics Subject Classification:42B10; 42B30; 42B35; 43A32 ; 44A35; 46F12; 46E35

show abstract

Boundedness and compactness of localization operators for Weinstein–Wigner transform

Cited by 21 publications

References 25 publications

The Weinstein transform associated with generalized distributions

The Weinstein transform associated with generalized distributions

Spectral theorems for Wigner transform associated with the Laguerre-Bessel localization operators

Extremal Functions on Generalized Weinstein Sobolev-gevrey spaces

Contact Info

Product

Resources

About