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Generalized Hermite Polynomials and the Heat Equation for Dunkl Operators

, 1997
Based on the theory of Dunkl operators, this paper presents a general concept of multivariable Hermite polynomials and Hermite functions which are associated with finite reflection groups on $\b R^N$.
Rösler, Margit
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Positivity of Dunkl’s intertwining operator

Duke Mathematical Journal, 1999
For a finite reflection group on $\b R^N,$ the associated Dunkl operators are parametrized first-order differential-difference operators which generalize the usual partial derivatives. They generate a commutative algebra which is - under weak assumptions - intertwined with the algebra of partial differential operators by a unique linear and homogeneous
openaire   +4 more sources

Markov Processes Related with Dunkl Operators

Advances in Applied Mathematics, 1998
Dunkl operators are differential-difference operators associated with a finite reflection group, acting on some Euclidean space, and they can be regarded as a generalization of partial derivatives and play a major role in the theory of quantum many-body systems.
Rösler, Margit, Voit, Michael
openaire   +2 more sources

Dirac Operators for the Dunkl Angular Momentum Algebra

Symmetry, Integrability and Geometry: Methods and Applications, 2022
We define a family of Dirac operators for the Dunkl angular momentum algebra depending on certain central elements of the group algebra of the Pin cover of the Weyl group inherent to the rational Cherednik algebra. We prove an analogue of Vogan's conjecture for this family of operators and use this to show that the Dirac cohomology, when non-zero ...
Calvert, Kieran, De Martino, Marcelo
openaire   +6 more sources

Poisson kernels of q$q$‐3D Hermite polynomials expansion for functions of several variables via generalized q$q$‐heat equations

Transactions of the London Mathematical Society, Volume 12, Issue 1, December 2025.
Abstract The representation of an analytic function as a series involving q$q$‐polynomials is a fundamental problem in classical analysis and approximation theory [Ramanujan J. 19 (2009), no. 3, 281–303]. In this paper, our investigation is focusing on q$q$‐analog complex Hermite polynomials, which were motivated by Ismail and Zhang [Adv. Appl.
Jian Cao
wiley   +1 more source

The singular and the 2:1 anisotropic Dunkl oscillators in the plane

, 2013
Two Dunkl oscillator models are considered: one singular and the other with a 2:1 frequency ratio. These models are defined by Hamiltonians which include the reflection operators in the two variables x and y.
Genest, Vincent X., Vinet, Luc, Zhedanov, Alexei   +2 more
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Elektronenspinresonanz an einzelnen Molekülen

Angewandte Chemie, Volume 137, Issue 37, September 8, 2025.
Dieser Minireview gibt einen Überblick über die vier Elektronenspinresonanz‐Techniken mit Einzelmolekül‐Empfindlichkeit, die entweder auf optisch detektierter Magnetresonanz oder Rastersondenmikroskopie basieren. Nach der Einführung der zugrunde liegenden gemeinsamen Konzepte wird ein Überblick über die jeweiligen Arbeitsprinzipien, experimentellen ...
Lisanne Sellies, Jascha Repp
wiley   +1 more source

Sharp estimates for potential operators associated with Laguerre and Dunkl-Laguerre expansions

, 2014
We study potential operators associated with Laguerre function expansions of convolution and Hermite types, and with Dunkl-Laguerre expansions. We prove qualitatively sharp estimates of the corresponding potential kernels.
Nowak, Adam, Stempak, Krzysztof
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Using the Dispersion of Apatite (U‐Th‐Sm)/He Single Grain Ages to Unravel the Burial and Exhumation History of the Foreland Basin of the Central Alps

Basin Research, Volume 37, Issue 5, September–October 2025.
We show that including provenance ages in thermochronometry modelling is key to arriving at a single consistent model explaining our complex dataset. With our approach, we reconcile previous studies on the northern Swiss Molasse Basin and contribute to the discussion of exhumation drivers. ABSTRACT Dispersed single‐grain ages are a common phenomenon in
Kevin A. Frings, Herfried Madritsch, Nicolas Villamizar‐Escalante, Peter A. Kukla, Christoph von Hagke   +4 more
wiley   +1 more source

Equivalence of the super Lax and local Dunkl operators for Calogero-like models

, 2004
Following Shastry and Sutherland I construct the super Lax operators for the Calogero model in the oscillator potential. These operators can be used for the derivation of the eigenfunctions and integrals of motion of the Calogero model and its ...
A I Neelov, Andrianov A A, Andrianov A A, Andrianov A A, Andrianov A A, Andrianov A A, Bordner A J, Brink L, Calogero F, Calogero F, Desrosiers P Lapointe L Mathieu P, Dunkl C F, Efthimiou C, Ghosh P, Hamermesh M, Inozemtsev V I Sasaki R, Ioffe M V, Ioffe M V, Khastgir S P, Komori Y, Komori Y, Lapointe L, Moser J, Nishino A, Nishino A, Pasquier V, Reed M, Ruhl W, Sutherland B, Sutherland B, Ujino H, Ujino H, Ujino H, Ujino H   +33 more
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