Related papers: Une $q$-d\'eformation de la transformation de Barg…
We obtain a $q$-linear analogue of Gegenbauer's expansion of the plane wave. It is expanded in terms of the little $q$-Gegenbauer polynomials and the \textit{third} Jackson $q$-Bessel function. The result is obtained by using a method based…
We revisit the old result that biflat Banach algebras have the same cyclic cohomology as $\mathbb C$, and obtain a quantitative variant (which is needed in forthcoming joint work of the author). Our approach does not rely on the…
Using deformations inspired by relativistic considerations and phase space symmetry, we deform the position and momentum operators in one dimension. The resulting algebra is shown to yield the q-oscillator algebra in one limiting case and…
Algebraic Bargmann and Darboux transformations for equations of a more general form than the Schr\"odinger ones with an additional functional dependence h(r) in the right-hand side of equations are constructed. The suggested generalized…
We discuss an extension of Toeplitz quantization based on polyanalytic functions. We derive isomorphism theorem for polyanalytic Toeplitz operators between weighted Sobolev-Fock spaces of polyanalytic functions, which are images of…
We give a formula for a $q$-analogue of Boyadzhiev-Mneimneh-type binomial sums of finite multi-polylogarithms. In the limit as $q\to 1$, this formula reduces to an identity equivalent to the Sakugawa-Seki identities. We also give a formula…
In this paper, we consider the degenerate Carlitz q-Bernoulli numbers and polynomials and we investigate some properties of those polynomials.
We study an asymptotic version of the Maslov-Hormander construction of Lagrangian distributions in terms of deformation quantization.
We develop a polynomial analogue of Meinardus' Thoerem for bivariate Euler products and apply it to the study of complex multiplicatively weighted partitions.
After introducing q-analogues of the Borel and Laplace transformations, we prove that to every formal power series solution of a linear q-difference equation with rational coefficients, we may apply several q-Borel and Laplace…
An integral transform for G=U(1,q) is studied. The transform maps the positive spin ladder representations of G on a Bargmann-Segal-Fock space F_n^1,q into a space of polynomial-valued functions on the bounded realization B^q of G/K. An…
We consider a linearized partial data Calder\'on problem for biharmonic operators extending the analogous result for harmonic operators. We construct special solutions and utilize Segal-Bargmann transform to recover lower order…
Analytic solutions and their formal asymptotic expansions for a family of the singularly perturbed $q-$difference-differential equations in the complex domain are constructed. They stand for a $q-$analog of the singularly perturbed partial…
We describe the range of of weighted Cauchy transform and its $k$-Bergman projection when action on weighted true poly-Bargmann spaces constituting an orthogonal Hilbertian decomposition of the Hilbert space of Gaussian functions on the…
We will introduce the notion of a near-isometric covariant representation of a $C^*$-correspondence and prove its Wold-type decomposition. Wold-type decomposition for doubly twisted left-invertible covariant representations of a product…
We extend the Bargmann transform to the magnetic pseudodifferential calculus, using gauge-covariant families of coherent states. We also introduce modulation mappings, a first step towards adapting modulation spaces to the magnetic case.
In this paper, we propose a new algebraic structure of permutation polynomials over $\mathbb{F}_{q^n}$. As an application of this new algebraic structure, we give some classes of new PPs over $\mathbb{F}_{q^n}$ and answer an open problem in…
We introduce two variants of $q$-hypergeometric equation. We obtain several explicit solutions of variants of $q$-hypergeometric equation. We show that a variant of $q$-hypergeometric equation can be obtained by a restriction of $q$-Appell…
Descent polynomials and peak polynomials, which enumerate permutations with given descent and peak sets respectively, have recently received considerable attention. We give several formulas for $q$-analogs of these polynomials which refine…
We obtain q-analogues of the Sylvester, Ces\`aro, Pasternack, and Bateman polynomials. We also derive generating functions for these polynomials.