we introduce a new concept of general $g$-$eta$-monotone operator generalizing the general $(h,eta)$-monotone operator cite{arvar2, arvar1}, general $h-$ monotone operator cite{xiahuang} in banach spaces, and also generalizing $g$-$eta$-monotone operator cite{zhang}, $(a, eta)$-monotone operator cite{verma2}, $a$-monotone operator cite{verma0}, $(h, eta)$-monotone operator cite{fanghuang}, $h$-...

Harmonic polynomials of type A are polynomials annihilated by the Dunkl Laplacian associated to the symmetric group acting as a reflection group on RN . The Dunkl operators are denoted by Tj for 1 ≤ j ≤ N, and the Laplacian ∆κ = ∑j=1 T2 j . This paper finds the homogeneous harmonic polynomials annihilated by all Tj for j > 2. The structure constants with respect to the Gaussian and sphere inner...

Recent studies show that deformations in quantum mechanics are inevitable. In this contribution, we consider a relativistic mechanical differential equation the presence of Dunkl operator-based deformation and investigate solutions for two important problems three-dimensional spatial space. To end, after introducing mechanics, examine Dunkl–Klein–Gordon oscillator with Cartesian spherical coord...

In this paper, we introduce and study a generalized Yosida approximation operator associated to H(·, ·)-co-accretive operator and discuss some of its properties. Using the concept of graph convergence and resolvent operator, we establish the convergence for generalized Yosida approximation operator. Also, we show an equivalence between graph convergence for H(·, ·)-co-accretive operator and gen...

We construct new solvable rational and trigonometric spin models with near-neighbors interactions by an extension of the Dunkl operator formalism. In the trigonometric case we obtain a finite number of energy levels in the center of mass frame, while the rational models are shown to possess an equally spaced infinite algebraic spectrum. For the trigonometric and one of the rational models, the ...

This paper consists in a first study of the Hardy space H in the rational Dunkl setting. Following Uchiyama’s approach, we characterizee H atomically and by means of the heat maximal operator. We also obtain a Fourier multiplier theorem for H. These results are proved here in the one-dimensional case and in the product case.

In this paper we prove inversion formulas for the Dunkl intertwining operator Vk and for its dual tVk and we deduce the expression of the representing distributions of the inverse operators V −1 k and V −1 k , and we give some applications.

This paper is intented to establish the analogue of Titchmarsh?s theorem for Dunkl generalized transform on real line.