Related papers: Non-Symmetric Askey--Wilson Shift Operators
We conjecture a geometrical form of the Paley-Wiener theorem for the Dunkl transform and prove three instances thereof, one of which involves a limit transition from Opdam's results for the graded Hecke algebra. Furthermore, the connection…
Recent work by several authors has revealed the existence of many unexpected classes of normal weighted composition operators. On the other hand, it is known that every normal operator is a complex symmetric operator. We therefore undertake…
We show that the method of separation of variables gives a natural generalisation of integral relations for classical special functions of one variable. The approach is illustrated by giving a new proof of the ``quadratic'' integral…
We develop a classification of composite operators without gradients at Anderson-transition critical points in disordered systems. These operators represent correlation functions of the local density of states (or of wave-function…
Symmetric functions appear in many areas of mathematics and physics, including enumerative combinatorics, the representation theory of symmetric groups, statistical mechanics, and the quantum statistics of ideal gases. In the commutative…
Heckman introduced $N$ operators on the space of polynomials in $N$ variables, such that these operators form a covariant set relative to permutations of the operators and variables, and such that Jack symmetric polynomials are…
A symmetric function of $N$ variables can be given in terms of symmetric polynomials of these variables. We determine those symmetric polynomials in which the dual differential operators take the neatest form when expressed in terms of our…
Based on the q-difference operators for the genus-two skein algebra, we show the correspondence between the reduced Askey-Wilson polynomials and the skein module of the genus-two handlebody.
Different analogs of quasiclassical limit for a q-oscillator which result in different (commutative and non-commutative) algebras of ``classical'' observables are derived. In particular, this gives the q-deformed Poisson brackets in terms…
We take advantage of the combinatorial interpretations of many sequences of polynomials of binomial type to define a sequence of symmetric functions corresponding to each sequence of polynomials of binomial type. We derive many of the…
In this paper, we introduce the so-called elliptic Askey-Wilson polynomials which are homogeneous polynomials in two special theta functions. With regard to the significance of polynomials of such kind, we establish some general elliptic…
The article is devoted to the investigation of operators on a non locally compact group algebra. Their isomorphisms are also studied.
The Heun-Askey-Wilson algebra is introduced through generators $\{\boX,\boW\}$ and relations. These relations can be understood as an extension of the usual Askey-Wilson ones. A central element is given, and a canonical form of the…
In this paper, we study Hamiltonian operators which are sum of a first order operator and of a Poisson tensor, in two spatial independent variables. In particular, a complete classification of these operators is presented in two and three…
In the present paper, we study the norms for symmetric and antisymmetric tensor products of weighted shift operators. By proving that for $n\geq 2$, $$\|S_{\alpha}^{l_1}\odot\cdots \odot S_{\alpha}^{l_k}\odot…
This article gives a brief introduction to $q$-special functions, i.e., $q$-analogues of the classical special functions. Here $q$ is a deformation parameter, usually $0<q<1$, where $q=1$ is the classical case. The main topics to be treated…
We propose a mechanism for calculating anomalous dimensions of higher-spin twist-two operators in N=4 SYM. We consider the ratio of the two-point functions of the operators and of their superconformal descendants or, alternatively, of the…
We investigate the relationship between the Bergman shift operator and the support of the corresponding measure. We pay special attention to the situation when the measure of orthogonality is concentrated on a polynomial lemniscate. As an…
We introduce braided Dunkl operators that are acting on a q-polynomial algebra and q-commute. Generalizing the approach of Etingof and Ginzburg, we explain the q-commutation phenomenon by constructing braided Cherednik algebras for which…
This paper provides a class of complex symmetric weighted composition operators on $H^2(\mathbb{D})$ to includes the unitary subclass, the Hermitian subclass and the normal subclass obtained by Bourdon and Noor. A characterization of…