In this paper, three-dimensional Dunkl oscillator models are studied in a generalized form of superintegrable Euclidean Hamiltonian systems to curved ones. These defined based on Hamiltonians, which depend deformation parameter underlying space and involve reflection operators. The corresponding symmetries obtained by the Jordan–Schwinger representations family Cayley–Klein orthogonal algebras ...

In this paper, the notion of closure operators of matroids  is generalized to fuzzy setting  which is called $M$-fuzzifying closure operators, and some properties of $M$-fuzzifying closure operators are discussed. The $M$-fuzzifying matroid induced by an $M$-fuzzifying closure operator can induce an $M$-fuzzifying closure operator. Finally, the characterizations of $M$-fuzzifying acyclic matroi...

In this paper, we introduce a notion of generalized states from an EQ-algebra E1 to another EQ-algebra E2, which is a generalization of internal states (or state operators) on an EQ-algebra E. Also we give a type of special generalized state from an EQ-algebra E1 to E1, called generalized internal states (or GI-state). Then we give some examples and basic properties of generalized (internal) st...

We continue a program generalizing classical results from the analysis on symmetric cones to Dunkl setting for root systems of type A A ...

We define the Littlewood-Paley decomposition associated with the Dunkl operators; from this decomposition we give the characterization of the Sobolev, Hölder and Lebesgue spaces associated with the Dunkl operators. We construct the paraproduct operators associated with the Dunkl operators similar to those defined by J.M. Bony in [1]. Using the LittlewoodPaley decomposition we establish the Sobo...

Abstract In this paper, we discuss a generalization to the Cherednik–Opdam integral operator an abstract space of Boehmians. We introduce sets Boehmians and establish delta sequences certain class convolution products. Then prove that extended is linear, bijective continuous with respect convergence generalized spaces Moreover, derive embeddings properties theory. obtain inversion formula provi...

Abstract. Assume that f is Dunkl polyharmonic in R (i.e. (∆h) f = 0 for some integer p, where ∆h is the Dunkl Laplacian associated to a root system R and to a multiplicity function κ, defined on R and invariant with respect to the finite Coxeter group). Necessary and successful condition that f is a polynomial of degree ≤ s for s ≥ 2p− 2 is proved. As a direct corollary, a Dunkl harmonic functi...

the rank-k numerical range has a close connection to the construction of quantum error correction code for a noisy quantum channel. for noisy quantum channel, a quantum error correcting code of dimension k exists if and only if the associated joint rank-k numerical range is non-empty. in this paper the notion of joint rank-k numerical range is generalized and some statements of [2011, generaliz...

For a family of weight functions invariant under a finite reflection group, we show how weighted Lp multiplier theorems for Dunkl transform on the Euclidean space Rd can be transferred from the corresponding results for hharmonic expansions on the unit sphere Sd of Rd+1. The result is then applied to establish a Hörmander type multiplier theorem for the Dunkl transform and to show the convergen...