Related papers: Fourier transforms on the quantum SU(1,1) group
In this paper, we generalize the weighted Fourier transform with respect to a function, originally proposed for the one-dimensional case in \cite{Dorrego}, to the $n$-dimensional Euclidean space $\mathbb{R}^{n}$. We develop a comprehensive…
Algebraic actions of unipotent groups $U$ actions on affine $k-$varieties $X$ ($k$ an algebraically closed field of characteristic 0) for which the algebraic quotient $X//U$ has small dimension are considered$.$ In case $X$ is factorial,…
The Harish-Chandra Fourier transform, $f\mapsto\mathcal{H}f,$ is a linear topological algebra isomorphism of the spherical (Schwartz) convolution algebra $\mathcal{C}^{p}(G//K)$ (where $K$ is a maximal compact subgroup of any arbitrarily…
The notion of Fourier transformation is described from an algebraic perspective that lends itself to applications in Symbolic Computation. We build the algebraic structures on the basis of a given Heisenberg group (in the general sense of…
Quantum Mechanics and Signal Processing in the line R, are strictly related to Fourier Transform and Weyl-Heisenberg algebra. We discuss here the addition of a new discrete variable that measures the degree of the Hermite functions and…
The emergence of the quantum $R$-matrix in the double-scaled SYK model points to an underlying quantum group structure. In this work, we identify the quantum group $\mathcal{U}_q(\mathfrak{su}(1,1))$ as a subalgebra of the chord algebra.…
In this paper we compute the spherical Fourier expansions coefficients for the restriction of the generalised Wendland functions from $d-$dimensional Euclidean space to the (d-1)-dimensional unit sphere. The development required to derive…
In this paper, we analyze a function space consisting of functions for which both the function and its Fourier transform exhibit Gaussian decay together with exponential growth governed by suitable weight functions. First, we examine…
In this article, we prove that (unit sphere, non-harmonic cone) is a Heisenberg uniqueness pair for the symplectic Fourier transform on $\mathbb C^n.$ We derive that spheres as well as non-harmonic cones are determining sets for the…
We generalize a number of works on the zeros of certain level 1 modular forms to a class of weakly holomorphic modular functions whose $q$-expansions satisfy \[ f_k(A, \tau) \colon = q^{-k}(1+a(1)q+a(2)q^2+...) + O(q),\] where $a(n)$ are…
In this work, we first give some mathematical preliminaries concerning the generalized prolate spheroidal wave function (GPSWFs). These set of special functions have been introduced in [16] and [7] and they are defined as the infinite and…
A novel generalization of the Askey-Wilson algebra is presented and shown to be associated with coproducts in the quantum algebra $U_q(su(1,1))$. This algebra has 15 non-commuting generators given by $Q^{(A)}$, with $A\subset \{1,2,3,4\}$…
We study certain overlap coefficients appearing in representation theory of the quantum algebra $\U_q(\mathfrak{sl}_2(\C))$. The overlap coefficients can be identified as products of Askey-Wilson functions, leading to an algebraic…
Let $L$ be a linear operator in $L^2(\mathbb{R}^n)$ which generates a semigroup $e^{-tL}$ whose kernels $p_t(x,y)$ satisfy the Gaussian upper bound. In this paper, we investigate several kinds of weighted norm inequalities for the conical…
The quantum Fourier transform (QFT) is a powerful tool in quantum computing. The main ingredients of QFT are formed by the Walsh-Hadamard transform H and phase shifts P(.), both of which are 2x2 unitary matrices as operators on the…
Three dimensional continuous and discrete Fourier-like transforms, based on the three simple and four semisimple compact Lie groups of rank 3, are presented. For each simple Lie group, there are three families of special functions ($C$-,…
We prove that functions with compact support in non-quasianalytic classes of Roumieu-type and of Beurling-type defined by a weight matrix with some mild regularity conditions can be characterized by the decay properties of their Fourier…
In this paper, we introduce and study the Fourier transform of functions which are integrable with respect to a vector measure on a compact group (not necessarily abelian). We also study the Fourier transform of vector measures. We also…
In this paper we consider the analytic continuation of the weighted Bergman spaces on the Lie ball $$\mathscr{D}=SO(2,n)/S(O(2) \times O(n))$$ and the corresponding holomorphic unitary (projective) representations of SO(2,n) on these…
Lecture notes for an eight hour course on quantum groups and $q$-special functions at the fourth Summer School in Differential Equations and Related Areas, Universidad Nacional de Colombia and Universidad de los Andes, Bogot\'a, Colombia,…