Related papers: Wirtinger operators for functions of several quate…

Recently, the conception of slice regular functions was allowed to introduce a new quaternionic functional calculus, among which the theory of semigroups of linear operators was developed into the quaternionic setting, even in a more…

We show that the half-line $m$ functions associated with the vector-valued Schrodinger operators are the elements in the Siegel upper half space. We introduce a metric on the space of $m$ functions associated to the vector-valued discrete…

This paper is in concern with Cauchy problems involving the fractional derivatives with respect to another function. Results of existence, uniqueness, and Taylor series among others are established in appropriate functional spaces. We prove…

Proper splittings of operators are commonly used to study the convergence of iterative processes. In order to approximate solutions of operator equations, in this article we deal with proper splittings of closed range bounded linear…

The aim of this paper is to extend the so called slice analysis to a general case in which the codomain is a real vector space of even dimension, i.e. is of the form $\mathbb{R}^{2n}$. We define a cone $\mathcal{W}_\mathcal{C}^d$ in…

We consider series expansions in bases of classical orthogonal polynomials. When such a series solves a linear differential equation with polynomial coefficients, its coefficients satisfy a linear recurrence equation. We interpret this…

We consider a natural basis of the Iwahori fixed vectors in the Whittaker model of an unramified principal series representation of a split semisimple p- adic group, indexed by the Weyl group. We show that the elements of this basis may be…

The purpose of this paper is to develop a new theory of three non-commuting quaternionic variables and its related Schur analysis theory for a modified version of the quaternionic global operator.

We prove a Nullstellensatz for the ring of polynomial functions in n non-commuting variables over Hamilton's ring of real quaternions. We also characterize the generalized polynomial identities in n variables which hold over the…

We study a generalization of the Wigner function to arbitrary tuples of hermitian operators, which is a distribution uniquely characterized by the property that the marginals for all linear combinations of the given operators agree with the…

The aim of this paper is to study some features of slice semi-regular functions $\mathcal{RM}(\Omega)$ on a circular domain $\Omega$ contained in the skew-symmetric algebra of quaternions $\mathbb{H}$ via the analysis of a family of linear…

We derive raising and lowering operators for orthogonal polynomials on the unit circle and find second order differential and $q$-difference equations for these polynomials. A general functional equation is found which allows one to relate…

We study cut-and-join operators for spin Hurwitz partition functions. We provide explicit expressions for these operators in terms of derivatives in $p$-variables without straightforward matrix realization, which is yet to be found. With…

Before we proposed an algebraic technics for the Hamiltonian approach to the evolution systems of partial differential equations, including systems with constraints. Here we further develop this approach and present the defining system of…

A crucial extension of quaternionic function theory to octonions is the concept of slice regular functions, introduced to handle holomorphic-like properties in a non-associative setting. In this paper, first we present a generalization of…

This paper gives a classification of first order polynomial differential operators of form $\mathscr{X} = X_1(x_1,x_2)\delta_1 + X_2(x_1,x_2)\delta_2$, $(\delta_i = \partial/\partial x_i)$. The classification is given through the order 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…

In their work on differential operators in positive characteristic, Smith and Van den Bergh define and study the derived functors of differential operators; they arise naturally as obstructions to differential operators reducing to positive…

We prove continuity properties of higher order commutators of fractional operators on the multilinear setting, between a product of weighted Lebesgue spaces into certain weighted Lipschitz spaces. The considered operators include the…

We study the effect of a splitting operator S_t on the L^p norm of the Fourier transform of a function f and on the operator norm of a Fourier multiplier m. Most of our results assume p is an even integer, and are often stronger when f or m…