Quantum Lax Pairs via Dunkl and Cherednik Operators
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DOI: 10.1007/s00220-019-03289-8
Abstract: We establish a direct link between Dunkl operators and quantum Lax matrices $${{\mathcal{L}}}$$L for the Calogero–Moser systems associated to an arbitrary Weyl group W (or an arbitrary finite reflection group in the rational case). This… read more here.
Keywords: cherednik operators; quantum lax; lax pairs; case ... See more keywords
Lipschitz and Triebel–Lizorkin spaces associated with the Dunkl operators on $$\mathbb {R}^d$$Rd
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DOI: 10.1007/s11117-019-00650-y
Abstract: In this paper we define Lipschitz and Triebel–Lizorkin spaces associated with the differential-difference Dunkl operators on $$\mathbb {R}^d$$Rd. We study inclusion relations among them. Next, some interpolation results and continuity results of some important operators… read more here.
Keywords: lizorkin spaces; triebel lizorkin; dunkl; lipschitz triebel ... See more keywords
Dunkl-supersymmetric orthogonal functions associated with classical orthogonal polynomials
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DOI: 10.1088/1751-8121/ab63a9
Abstract: We consider the eigenvalue problem associated with the Dunkl-type differential operator (in which the reflection operator R is involved) L = dx R + v(x), (v(-x) = -v(x)), in the context of supersymmetric quantum mechanical… read more here.
Keywords: dunkl supersymmetric; orthogonal polynomials; dunkl; supersymmetric orthogonal ... See more keywords
Fractional Smoothness in Lp with Dunkl Weight and Its Applications
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DOI: 10.1134/s0001434619090232
Abstract: We define fractional power of the Dunkl Laplacian, fractional modulus of smoothness and fractional $K$-functional in $L^p$-space with the Dunkl weight. As application, we prove direct and inverse theorems of approximation theory, and some inequalities… read more here.
Keywords: fractional smoothness; weight applications; dunkl; smoothness dunkl ... See more keywords