相关论文: Commuting difference operators with applications t…
In this paper we explore solvability of steady-state variational inequalities with multivalued operators. Moreover, we are studying the connections between the class of radially semi-continuous operators with semi-bounded variation and…
The linearization coefficients for a set of orthogonal polynomials are given explicitly as a weighted sum of combinatorial objects. Positivity theorems of Askey and Szwarc are corollaries of these expansions.
Motivated by the work of Visontai and Dey-Sivasubramanian on the gamma-positivity of some polynomials, we find the commutative property of a pair of Eulerian operators. As an application, we show the bi-gamma-positivity of the descent…
We introduce a new family of special functions, namely $q$-Charlier multiple orthogonal polynomials. These polynomials are orthogonal with respect to $q$-analogues of Poisson distributions. We focus our attention on their structural…
We study two families of orthogonal polynomials. The first is a finite family related to the Askey-Wilson polynomials but the orthogonality is on the real line. A limiting case of this family is an infinite system of orthogonal polynomials…
Integration of nonlinear partial differential equations with the help of the non-commutative integration over octonions is studied. An apparatus permitting to take into account symmetry properties of PDOs is developed. For this purpose…
In this paper we continue to investigate a certain class of Hankel-like positive definite kernels using their associated orthogonal polynomials. The main result of this paper is about the structure of this kind of kernels.
The Schr\"odinger operators with exchange terms for certain Calogero-Sutherland quantum many body systems have eigenfunctions which factor into the symmetric ground state and a multivariable polynomial. The polynomial can be chosen to have…
We give an algebraic construction of shift operators for the non-symmetric Heckman-Opdam polynomials and the non-symmetric Macdonald-Koornwinder polynomials. To each linear character of the finite Weyl group, we associate forward and…
We study the phenomena that arise when we combine the standard pseudodifferential operators with those operators that appear in the study of some sub-elliptic estimates, and on strongly pseudoconvex domains. The algebra of operators we…
Motivated by the differential basis theorem of Kolchin and the difference-differential basis theorem of Cohn, in this paper we present a basis theorem for polynomial rings equipped with commuting generalised Hasse-Schmidt operators (in the…
We construct new families of discrete vector orthogonal polynomials that have the property to be eigenfunctions of some difference operator. They are extensions of Charlier, Meixner and Kravchuk polynomial systems. The ideas behind our…
In this paper, we present a new method via the transfer matrix approach to obtain asymptotic formulae of orthogonal polynomials with asymptotically identical coefficients of bounded variation. We make use of the hyperbolicity of the…
We give two examples of algebras of differential operators associated to families of matrix valued orthogonal polynomials arising from representations of SU$(N+1)$. The first one gives a commutative algebra and the second one a…
A LG-WKB and Turning point theory is developed for three term recurrence formulas associated with monotonic recurrence coefficients. This is used to find strong asymptotics for certain classical orthogonal polynomials including Wilson…
We study matrix three term relations for orthogonal polynomials in two variables constructed from orthogonal polynomials in one variable. Using the three term recurrence relation for the involved univariate orthogonal polynomials, the…
Heckman-Polychronakos operators form a prominent family of commuting differential-difference operators defined in terms of the Dunkl operators $\mathcal D_i$ as $\mathcal P_m= \sum_{i=1}^N (x_i \mathcal D_i)^m$. They have been known since…
We consider dual polynomials of the multi-indexed ($q$-)Racah orthogonal polynomials. The $M$-indexed ($q$-)Racah polynomials satisfy the second order difference equations and various $1+2L$ ($L\geq M+1$) term recurrence relations with…
This paper defines and investigates nonsymmetric Macdonald polynomials with values in an irreducible module of the Hecke algebra of type $A_{N-1}$. These polynomials appear as simultaneous eigenfunctions of Cherednik operators. Several…
We study skew-orthogonal polynomials with respect to the weight function $\exp[-2V(x)]$, with $V(x)=\sum_{K=1}^{2d}(u_{K}/{K})x^{K}$, $u_{2d} > 0$, $d > 0$. A finite subsequence of such skew-orthogonal polynomials arising in the study of…