Related papers: Slice regular composition operators
The $S$-functional calculus is based on the theory of slice hyperholomorphic functions and it defines functions of $n$-tuples of not necessarily commuting operators or of quaternionic operators. This calculus relays on the notion of…
The aim of this paper is to present the application of an approach to study contraction theory recently developed for piecewise smooth and switched systems. The approach that can be used to analyze incremental stability properties of…
We study possibilities for algebraic closures, differences between definable and algebraic closures in first-order structures, and variations of these closures with respect to the bounds of cardinalities of definable sets and given sets of…
In this paper we study the additive splitting associated to the quaternionic Cauchy transform defined by the Cauchy formula of slice hyperholomorphic functions. Moreover, we introduce and study the analogue of the fundamental solution of…
A generalization of the classical Lipschitz summation formula is proposed. It involves new polylogarithmic rational functions constructed via the Fourier expansion of certain sequences of Bernoulli--type polynomials. Related families of…
The existence of topologically slice knots that are of infinite order in the knot concordance group followed from Freedman's work on topological surgery and Donaldson's gauge theoretic approach to 4-manifolds. Here, as an application of…
A decomposition theorem for self-adjoint operators proved by Riesz and Lorch is extended to normal operators. This extension gives a new proof of the spectral theorem for unbounded normal operators.
We follow the general recipe for constructing commutative families of $W$-operators, which provides Hurwitz-like expansions in symmetric functions (Macdonald polynomials), in order to obtain a difference operator example that gives rise to…
We introduce an operator on classes of regular languages, the star-free closure. Our motivation is to generalize standard results of automata theory within a unified framework. Given an arbitrary input class $C$, the star-free closure…
In this article, we study the weighted composition operators preserving the class $\mathcal{P}_{\alpha}$ of analytic functions subordinate to $\frac{1+\alpha z}{1-z}$ for $|\alpha|\leq 1, \alpha \neq -1$. Some of its consequences and…
The theme of this work is that the theory of charged particles in a uniform magnetic field can be generalized to a large class of operators if one uses an extended a class of Weyl operators which we call "Landau--Weyl pseudodifferential…
The piecewise-concave function may be used to approximate a wide range of other functions to arbitrary precision over a bounded set. In this short paper, this property is proven for three function classes: (a) the multivariate twice…
We study the commutation relations and normal ordering between families of operators on symmetric functions. These operators can be naturally defined by the operations of multiplication, Kronecker product, and their adjoints. As…
This paper deals with a certain class of second-order conformally invariant operators acting on functions taking values in particular (finite-dimensional) irreducible representations of the orthogonal group. These operators can be seen as a…
We study projective functions. We prove that projective functions generalise lower and upper-semianalytic ones while being stable by composition and difference. We show that the class of projective functions is closed under sums,…
We generalize the classical notion of adjoint of a linear operator and the Aron-Schottenloher notion of adjoint of a homogeneous polynomial. The general notion is shown to enjoy several properties enjoyed by the classical ones, nevertheless…
Let W be the complex reflection group G(e,1,n). In the author's previous paper, Hall-Littlewood functions associated to W were introduced. In the special case where W is a Weyl group of type B_n, they are closely related to Green…
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…
A classical theorem due to G.D. Birkhoff states that there exists an entire function whose translates approximate any given entire function, as accurately as desired, over any ball of the complex plane. We show this result may be…
We give a new proof that every linear fractional map of the unit ball induces a bounded composition operator on the standard scale of Hilbert function spaces on the ball, and obtain norm bounds analogous to the standard one-variable…