相关论文: Raising and Lowering Operators for Askey-Wilson Po…
The numerical evaluation of an individual Bessel or Hankel function of large order and large argument is a notoriously problematic issue in physics. Recurrence relations are inefficient when an individual function of high order and argument…
In 1991 Tratnik derived two systems of multivariable orthogonal Wilson polynomials and considered their limit cases. q-Analogues of these systems are derived, yielding systems of multivariable orthogonal Askey-Wilson polynomials and their…
The present article is concerned with global subelliptic estimates for Kramers-Fokker-Planck operators with polynomials of degree less than or equal to two. The constants appearing in those estimates are accurately formulated in terms of…
We give a direct proof of the equivalence between the Giambelli and Pieri type formulas for Hall-Littlewood functions using Young's raising operators, parallel to joint work with Buch and Kresch for the Schubert classes on isotropic…
The simple algebras of a dressed operator, which is composed of a dressing and a residual operators, are averaged following a proper statistics of the dressing one. In the Bose-Einstein statistics, a (fermionic) Calogero-Vasiliev…
We prove a general quadratic formula for basic hypergeometric series, from which simple proofs of several recent determinant and Pfaffian formulas are obtained. A special case of the quadratic formula is actually related to a Gram…
This paper presents a method for constructing flat deformations of associative algebras. We will refer to this method as method two because it is a generalisation of the method obtained in [1]. The deformations obtained using the first two…
We establish a q-generalization of Gordon's theorem that the space of diagonal coinvariants has a quotient identified with a perfect representation of the rational double affine Hecke algebra. It leads to a simple proof of his theorem and…
The q-difference analog of the classical ladder operators is derived for those orthogonal polynomials arising from a class of indeterminate moments problem.
We consider multiple orthogonal polynomials with respect to two modified Jacobi weights on touching intervals [a,0] and [0,1], with a < 0, and study a transition that occurs at a = -1. The transition is studied in a double scaling limit,…
Motivated by Liu's recent work in \cite{Liu2022}. We shall reveal the essential feature of Hahn polynomials by presenting two new $q$-exponential operators. These lead us to use a systematic method to study identities involving Hahn…
The operators of fractional calculus come in many different types, which can be categorised into general classes according to their nature and properties. We conduct a formal study of the class known as weighted fractional calculus and its…
In this paper, we derive new recurrence relations for two-variable orthogonal polynomials for example Jacobi polynomial, Bateman's polynomial and Legendre polynomial via two different differential operators $\Xi =\left(\frac{\partial…
We present some 2-isometric lifting and extension results for Hilbert space concave operators. For a special class of concave operators we study their Cauchy dual operators and discuss conditions under which these operators are subnormal.…
In this work we show how to get advantage from the Riemann--Hilbert analysis in order to obtain first and second order differential equations for the orthogonal polynomials and associated functions with a weight on the unit circle. We…
The point-splitting regularization technique for composite operators is discussed in connection with anomaly calculation. We present a pedagogical and self-contained review of the topic with an emphasis on the technical details. We also…
We derive generalized generating functions for basic hypergeometric orthogonal polynomials by applying connection relations with one free parameter to them. In particular, we generalize generating functions for the Askey-Wilson, continuous…
We introduce two q-analogues of the 2D-Hermite polynomials which are functions of two complex variables. We derive explicit formulas, orthogonality relations, raising and lowering operator relations, generating functions, and Rodrigues…
In this paper we study two-sided (left and right) axially symmetric solutions of a generalized Cauchy-Riemann operator. We present three methods to obtain special solutions: via the Cauchy-Kowalevski extension theorem, via plane wave…
We prove that the scalar and $2\times 2$ matrix differential operators which preserve the simplest scalar and vector-valued polynomial modules in two variables have a fundamental Lie algebraic structure. Our approach is based on a general…