Results 11 to 20 of about 454,230 (160)
Dunkl wavelets and applications to inversion of the Dunkl intertwining operator and its dual [PDF]
International Journal of Mathematics and Mathematical Sciences, 2004 We define and study Dunkl wavelets and the corresponding Dunkl wavelets transforms, and we prove for these transforms Plancherel and reconstruction formulas. We give as application the inversion of the Dunkl intertwining operator and its dual.
Abdellatif Jouini
doaj +5 more sources
Dunkl Operators: Theory and Applications [PDF]
, 2003 These lecture notes are intended as an introduction to the theory of rational Dunkl operators and the associated special functions, with an emphasis on positivity and asymptotics. We start with an outline of the general concepts: Dunkl operators, the intertwining operator, the Dunkl kernel and the Dunkl transform.
Rosler, M., Koelink, Erik
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Dunkl Translation and Uncentered Maximal Operator on the Real Line [PDF]
International Journal of Mathematics and Mathematical Sciences, 2007 We establish estimates of the Dunkl translation of the characteristic function χ[−ɛ,ɛ], ɛ>0, and we prove that the uncentered maximal operator associated with the Dunkl operator is of weak type (1,1).
Chokri Abdelkefi, Mohamed Sifi
doaj +2 more sources
Necessary and Sufficient Conditions for the Boundedness of Dunkl-Type Fractional Maximal Operator in the Dunkl-Type Morrey Spaces [PDF]
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. We study the boundedness of the Dunkl-type fractional maximal operator 𝑀𝛽 in the Dunkl-type Morrey space 𝐿𝑝,𝜆,𝛼(ℝ), 0 ...
Emin Guliyev +2 more
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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.
Ivan H. Dimovski, Valentin Z. Hristov
doaj +5 more sources
Dunkl convolution and elliptic regularity for Dunkl operators
Mathematische Nachrichten, Volume 297, Issue 12, Page 4416-4436, December 2024.Abstract We discuss in which cases the Dunkl convolution u∗kv$u*_kv$ of distributions u,v$u,v$, possibly both with non‐compact support, can be defined and study its analytic properties. We prove results on the (singular‐)support of Dunkl convolutions.
Dominik Brennecken
wiley +4 more sources
Oscillation inequalities for Carleson–Dunkl operator [PDF]
Rendiconti del Circolo Matematico di Palermo Series 2Abstract In this paper, we establish estimates for the oscillation seminorm for the so-called Carleson–Dunkl operator on weighted $$L^p(\mathbb {R},w(x)|x|^{2\alpha +1}\textrm{d}x)$$ L p
Słomian, Wojciech
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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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Bernoulli–Dunkl and Apostol–Euler–Dunkl polynomials with applications to series involving zeros of Bessel functions [PDF]
, 2018 We introduce Bernoulli–Dunkl and Apostol–Euler–Dunkl polynomials as generalizations of Bernoulli and Apostol–Euler polynomials, where the role of the derivative is now played by the Dunkl operator on the real line.
Pérez, Mario +11 more
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