Related papers: A q deformation of true-polyanalytic Bargmann tran…
By generating function based on the Jackson's q-exponential function and standard exponential function, we introduce a new q-analogue of Hermite and Kampe-de Feriet polynomials. In contrast to standard Hermite polynomials, with triple…
This work continues the research of generalized Heisenberg algebras connected with several orthogonal polynomial systems. The realization of the annihilation operator of the algebra corresponding to a polynomial system by a differential…
In this article, we exhaustively explore the terminating basic hypergeometric representations and transformations of the $q$ and $q^{-1}$-symmetric subfamilies of the Askey--Wilson polynomials. These subfamilies are obtained by repeatedly…
For the two-parameter $p,q$-deformed Heisenberg algebra introduced recently and in which, instead of usual commutator of $X$ and $P$ in the l.h.s. of basic relation $[X,P] = {\rm i}\hbar$, one uses the $p,q$-commutator, we established…
A wide class of q-deformed harmonic oscillators including those of Macfarlane type and of Dubna type is shown to be describable in a unified way. The Hamiltonian of the oscillator is assumed to be given by a q-deformed anti-commutator of…
A new class of bivariate poly-analytic Hermite polynomials is considered. We show that they are realizable as the Fourier-Wigner transform of the univariate complex Hermite functions and form a nontrivial orthogonal basis of the classical…
The $q$-deformed Bannai-Ito algebra was recently constructed in the threefold tensor product of the quantum superalgebra $\mathfrak{osp}_q(1\vert 2)$. It turned out to be isomorphic to the Askey-Wilson algebra. In the present paper these…
We use Berezin's quantization procedure to obtain a formal $U_q su_{1,1}$-invariant deformation of the quantum disc. Explicit formulae for the associated q-bidifferential operators are produced.
We set up a framework for discussing `$q$-analogues' of the usual covariant differential operators for hermitian symmetric spaces. This turns out to be directly related to the deformation quantization associated to quadratic algebras…
We have introduced a q-deformation, i.e., a polynomial in q with natural coefficients, of the binomial coefficient of two finite words u and v counting the number of occurrences of v as a subword of u. In this paper, we examine the…
A $\gamma$-deformed version of $su(2)$ algebra with non-hermitian generators has been obtained from a bi-orthogonal system of vectors in $\bf{C^2}$. The related Jordan-Schwinger(J-S) map is combined with boson algebras to obtain a hierarchy…
We discuss how a q-mutation relation can be deformed replacing a pair of conjugate operators with two other and unrelated operators, as it is done in the construction of pseudo-fermions, pseudo-bosons and truncated pseudo-bosons. This…
We use the Poisson kernel of the continuous $q$-Hermite polynomials to introduces families of integral operators, which are semigroups of linear operators. We describe the eigenvalues and eigenfunctions of one family of operators. The…
Within the standard quantum mechanics a q-deformation of the simplest N=2 supersymmetry algebra is suggested. Resulting physical systems do not have conserved charges and degeneracies in the spectra. Instead, superpartner Hamiltonians are…
Creation operators are given for the three distinguished bases of the type BCD universal character ring of Koike and Terada yielding an elegant way of treating computations for all three types in a unified manner. Deformed versions of these…
We introduce a notion of $q$-deformed rational numbers and $q$-deformed continued fractions. A $q$-deformed rational is encoded by a triangulation of a polygon and can be computed recursively. The recursive formula is analogous to the…
Recently, Morier-Genoud and Ovsienko introduced a $q$-deformation of rational numbers. More precisely, for an irreducible fraction $\frac{r}s>0$, they constructed coprime polynomials $\mathcal{R}_{\frac{r}s}(q),~ \mathcal{S}_{\frac{r}s}(q)…
Quantum signal processing is a powerful framework in quantum algorithms, playing a central role in Hamiltonian simulation and related applications. The sequence of polynomials implemented at each step of this protocol provides a polynomial…
We obtain weight functions associated with $q$-linear and $q$-quadratic lattices that yield discrete orthogonality with respect to a quasi-definite moment functional for the Askey-Wilson polynomials and all the polynomial sequences in the…
In this paper, we establish a q-analog of partial fraction decomposition formula. By using formula, we develop new closed form representations of sums of q-harmonic numbers and reciprocal q-binomial coefficients. Moreover, we give explicit…