In this paper, we investigate the well-posedness for Cauchy problem multi-term time-fractional heat equation associated with Dunkl operator. The under consideration includes a linear combination of Caputo derivatives in time decreasing orders (0, 1) and positive constant coefficients one-dimensional operator.  To show solvability problem  use several important properties multinomial M...

We generate solvable cases of the two angular equations resulting from variable separation in three-dimensional Dunkl-Schrödinger equation expressed spherical coordinates. It is shown that Dunkl formalism interrelates these with trigonometric Pöschl-Teller systems. Based on this interrelation, we use point transformations and Darboux-Crum to construct new equations. Instead stationary energy, c...

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 supersymmetric version. They allow to infer several relations involving the Lax matrices for this model in a fast way. It is shown that the super Lax ope...

In this paper, we consider the normalized Bessel function of index ?>?12, find an integral representation term xnj?+n(x)j?(y). This allows us to establish a product formula for generalized Hankel B??,n on R. is kernel transform F?,n arising from Dunkl theory. Indeed show that B??,n(x)B??,n(y) can be expressed as in terms B??,n(z) with explicit invoking Gegenbauer polynomials all n?N?. The obtai...

We study approximation properties of weighted $\mathrm{L}^2$-orthogonal projectors onto spaces polynomials bounded degree in the Euclidean unit ball, where weight is reflection-invariant form $(1-\lVert x \rVert^2)^\alpha \prod_{i=1}^d \lvert x_i \rvert^{\gamma_i}$, $\alpha, \gamma_1, \dots, \gamma_d > -1$. Said are measured Dunkl-Sobolev-type norms which same $\mathrm{L}^2$ norm used to contro...

We construct several new families of exactly and quasi-exactly solvable BCN -type Calogero– Sutherland models with internal degrees of freedom. Our approach is based on the introduction of a new family of Dunkl operators of BN type which, together with the original BN -type Dunkl operators, are shown to preserve certain polynomial subspaces of finite dimension. We prove that a wide class of qua...

We investigate algebraic structure for the BN -type Calogero model by using the exchange-operator formalism. We show that the set of the Jack polynomials whose arguments are Dunkl-type operators provides an orthogonal basis.