Results 1 to 10 of about 2,869 (96)
Dunkl–Schrödinger Operators [PDF]
Complex Analysis and Operator Theory, 2018 In this paper, we consider the Schrödinger operators $L_k=-Δ_k+V$, where $Δ_k$ is the Dunkl-Laplace operator and $V$ is a non-negative potential on $R^d$. We establish that $L_k $ is essentially self-adjoint on $C_0^\infty$. In particular, we develop a bounded $H^\infty$-calculus on $L^p$ spaces for the Dunkl harmonic oscillator operator.
Béchir Amri
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Semigroup and Riesz transform for the Dunkl–Schrödinger operators [PDF]
Semigroup Forum, 2020 Let $L_k=-Δ_k+V$ be the Dunk- Schrödinger operators, where $Δ_k=\sum_{j=1}^dT_j^2$ is the Dunkl Laplace operator associated to the dunkl operators $T_j$ on $\mathbb{R}^d$ and $V$ is a nonnegative potential function. In the first part of this paper we introduce the Riesz transform $R_j= T_j L_k^{-1/2}$ as an $L^2$- bounded operator and we prove that is ...
Béchir Amri
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Dunkl generalization of Szász beta‐type operators [PDF]
Mathematical Methods in the Applied Sciences, 2017 The goal in the paper is to advertise Dunkl extension of Szász beta‐type operators. We initiate approximation features via acknowledged Korovkin and weighted Korovkin theorem and obtain the convergence rate from the point of modulus of continuity, second‐order modulus of continuity, the Lipschitz class functions, Peetre's K‐functional, and modulus of ...
Bayram ÇEkim +2 more
exaly +4 more sources
Nonlocal Operational Calculi for Dunkl Operators [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2009 The one-dimensional Dunkl operator $D_k$ with a non-negative parameter $k$, is considered under an arbitrary nonlocal boundary value condition. The right inverse operator of $D_k$, satisfying this condition is studied. An operational calculus of Mikusinski type is developed.
Dimovski, Ivan H., Hristov, Valentin Z.
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Dunkl operators for arbitrary finite groups [PDF]
Advances in Operator Theory, 2021 New example using Cuntz algebras, final version, 44 ...
Micho Đurđevich, Stephen Bruce Sontz
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Inversion Formulas for the Dunkl Intertwining Operator and Its Dual on Spaces of Functions and Distributions [PDF]
, 1998 In this paper we prove inversion formulas for the Dunkl intertwining operator $V_k$ and for its dual ${}^tV_k$ and we deduce the expression of the representing distributions of the inverse operators $V_k^{-1}$ and ${}^tV_k^{-1}$, and we give some ...
Broglia, R.A. +4 more
core +10 more sources
Inversion Formulas for the Spherical Radon-Dunkl Transform [PDF]
, 2009 The spherical Radon-Dunkl transform $R_\kappa$, associated to weight functions invariant under a finite reflection group, is introduced, and some elementary properties are obtained in terms of $h$-harmonics.
Li, Zhongkai, Song, Futao
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DUNKL OPERATORS FOR COMPLEX REFLECTION GROUPS [PDF]
Proceedings of the London Mathematical Society, 2003 Dunkl operators for complex reflection groups are defined in this paper. These commuting operators give rise to a parameterized family of deformations of the polynomial De Rham complex. This leads to the study of the polynomial ring as a module over the ‘rational Cherednik algebra’, and a natural contravariant form on this module.
Dunkl, C.F., Opdam, E.M.
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Dunkl Operators as Covariant Derivatives in a Quantum Principal Bundle [PDF]
, 2013 A quantum principal bundle is constructed for every Coxeter group acting on a finite-dimensional Euclidean space $E$, and then a connection is also defined on this bundle.
Durdevich, Micho, Sontz, Stephen Bruce
core +5 more sources
Generalized Dunkl operator [PDF]
Ufimskii Matematicheskii Zhurnal, 2014 In the paper we introduce a generalized Dunkl operator acting in the space of entire functions on C. We study problems of harmonic analysis related with this operator and show its connection with the Gelfond-Leont'ev operator of generalized differentiation.
Il'mir Irshatovich Karamov +1 more
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