Results 11 to 20 of about 2,908 (161)
Dunkl convolution and elliptic regularity for Dunkl operators
Mathematische NachrichtenAbstractWe discuss in which cases the Dunkl convolution of distributions , possibly both with non‐compact support, can be defined and study its analytic properties. We prove results on the (singular‐)support of Dunkl convolutions. Based on this, we are able to prove a theorem on elliptic regularity for a certain class of Dunkl operators, called ...
Dominik Brennecken
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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.
Amri, Béchir, Hammi, Amel
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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
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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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A Class of Quantum Briot–Bouquet Differential Equations with Complex Coefficients
Mathematics, 2020 Quantum inequalities (QI) are local restraints on the magnitude and range of formulas. Quantum inequalities have been established to have a different range of applications. In this paper, we aim to introduce a study of QI in a complex domain.
Rabha W. Ibrahim +2 more
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The Dunkl kernel and intertwining operator for dihedral groups
, 2020 Dunkl operators associated with finite reflection groups generate a commutative algebra of differential-difference operators. There exists a unique linear operator called intertwining operator which intertwines between this algebra and the algebra of ...
De Bie, Hendrik, Lian, Pan
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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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Some Embeddings into the Morrey and Modified Morrey Spaces Associated with the Dunkl Operator
Abstract and Applied Analysis, 2010 We consider the generalized shift operator, associated with the Dunkl operator Λα(f)(x)=(d/dx)f(x)+((2α+1)/x)((f(x)-f(-x))/2), α>-1/2.
Emin V. Guliyev, Yagub Y. Mammadov
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Математичні Студії, 2022 In the present investigation, inspired by the work on Yamaguchi type class of analytic functions satisfyingthe analytic criteria $\mathfrak{Re}\{\frac{f (z)}{z}\} > 0, $ in the open unit disk $\Delta=\{z \in \mathbb{C}\colon |z|
T. Panigrahi, G. Murugusundaramoorthy
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