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This paper is inspired by a class of infinite order differential operators arising in the time evolution of superoscillations. Recently, infinite order differential operators have been considered and characterized on the spaces of entire…
Infinite order differential operators appear in different fields of Mathematics and Physics and in the last decades they turned out to be of fundamental importance in the study of the evolution of superoscillations as initial datum for…
We study infinite order differential operators acting in the spaces of exponential type entire functions. We derive conditions under which such operators preserve the set of Laguerre entire functions which consists of the polynomials…
This paper grew out of the author's work on arXiv:2504.18460. Differential operators in the sense of Grothendieck acting between modules over a commutative ring can be interpreted as torsion elements in the bimodule of all operators with…
In this paper, we consider the locally convex spaces of entire functions with growth given by proximate orders, and study the representation as a differential operator of a continuous homomorphism from such a space to another one. As a…
We develop a theory of pseudodifferential operators of infinite order for the global classes $\mathcal{S}_{\omega}$ of ultradifferentiable functions in the sense of Bj\"orck, following the previous ideas given by Prangoski for…
This paper studies a particular class of higher order conformally invariant dif- ferential operators and related integral operators acting on functions taking values in particular finite dimensional irreducible representations of the Spin…
Specific global symbol classes and corresponding pseudodifferential operators of infinite order that act continuously on the space of tempered ultradistributions of Beurling and Roumieu type are constructed. For these classes, symbolic…
Superoscillations are a phenomenon in physics, where linear combinations of low-frequency plane waves interfere almost destructively in such a way that the resulting wave has a higher frequency than any of the individual waves. The…
The aim of this paper is to characterize continuous endomorphisms in the space of entire functions of exponential type of order $p>0$. Let $A_p$ denote the space of entire functions of $n$ complex variables $z\in{\mathbb C}^n$ of order $p$…
In recent years, the study of slice monogenic functions has attracted more and more attention in the literature. In this paper, an extension of the well-known Dirac operator is defined which allows to establish the Lie superalgebra…
This paper is dedicated to the construction of multidimensional spherical monogenics. Firstly, we investigate the construction of monogenic functions in dimension $3$ by applying the Dirac operator to the orthonormal bases of spherical…
In this article, we present the symmetry group of a global slice Dirac operator and its iterated ones. Further, the explicit forms of intertwining operators of the iterated global slice Dirac operator are given. At the end, we introduce a…
In this article, we conduct a study of integral operators defined in terms of non-convolution type kernels with singularities of various degrees. The operators that fall within our scope of research include fractional integrals, fractional…
The elements of the class of non-homogeneous differential operators which are based on the same vector field, when viewed as acting on appropriate Hilbert spaces, are shown to be isomorphic to each other. It shown that the replacement of a…
In this paper we construct a large class of multiplication operators on reproducing kernel Hilbert spaces which are {\em homogeneous} with respect to the action of the M\"{o}bius group consisting of bi-holomorphic automorphisms of the unit…
We emphasize some properties of coherent state groups, i.e. groups whose quotient with the stationary groups, are manifolds which admit a holomorphic embedding in a projective Hilbert space. We determine the differential action of the…
A hypergeometric type equation satisfying certain conditions defines either a finite or an infinite system of orthogonal polynomials. The associated special functions are eigenfunctions of some shape invariant operators. These operators can…
In this paper we describe a general method to generate superoscillatory functions of several variables starting from a superoscillating sequence of one variable. Our results are based on the study of suitable infinite order differential…
Potential algebras can be used effectively in the analysis of the quantum systems. In the article, we focus on the systems described by a separable, 2x2 matrix Hamiltonian of the first order in derivatives. We find integrals of motion of…