Related papers: Characterization of continuous homomorphisms on en…
In 2016, the spectral theory on the $S$-spectrum was used to establish the $H^\infty$-functional calculus for quaternionic or Clifford operators. This calculus applies for example to sectorial or bisectorial right linear operators $T$ and…
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…
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…
In this paper, a criterion for a sequence of composition operators defined on the space of holomorphic functions in a complex domain to be frequently hypercyclic is provided. Such criterion improves some already known special cases and, in…
We study algebras of bounded noncommutative (nc) functions on unit balls of operator spaces (nc operator balls) and on their subvarieties. Considering the example of the nc unit polydisk we show that these algebras, while having a natural…
In this paper, using the tools from the lineability theory, we distinguish certain subsets of $p$-adic differentiable functions. Specifically, we show that the following sets of functions are large enough to contain an infinite dimensional…
Quaternionic Clifford analysis is a recent new branch of Clifford analysis, a higher dimensional function theory which refines harmonic analysis and generalizes to higher dimension the theory of holomorphic functions in the complex plane.…
In this paper, we lay the foundations of the theory of slice regular functions in several variables ranging in any real alternative $^*$-algebra, including quaternions, octonions and Clifford algebras. This theory is an extension of the…
Monogenic functions are basic to Clifford analysis. On Euclidean space they are defined as smooth functions with values in the corresponding Clifford algebra satisfying a certain system of first order differential equations, usually…
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 foundation of spectral theory on the $S$-spectrum can be traced back to the quaternionic framework of quantum mechanics. The concept of $S$-spectrum for quaternionic operators emerged as the natural spectrum in slice hyperholomorphic…
In this paper we investigate some basic results on the slice regular Besov spaces of hyperholomorphic functions on the unit ball $\mathbb{B}.$ We also characterize the boundedness, compactness and find the essential norm estimates of…
We study the character of the infinite wedge projective representation of the algebra of differential operators on the circle. We prove quasi-modularity of this character and also compute certain generating functions for traces of…
The spectral theory on the $S$-spectrum originated to give quaternionic quantum mechanics a precise mathematical foundation and as a spectral theory for linear operators in vector analysis. This theory has proven to be significantly more…
Let $A$ be one of the following Clifford algebras : $\mathbb{R}_2 \cong \mathbb{H}$ or $\mathbb{R}_3$. For the algebra $A$, the automorphism group $Aut(A)$ and its invariants are well known. In this paper we will describe the invariants of…
We extend constructions of classical Clifford analysis to the case of indefinite non-degenerate quadratic forms. We define (p,q)-left- and right-monogenic functions by means of Dirac operators that factor a certain wave operator. We prove…
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…
Let $\mathcal{H}$ be a complex infinite dimensional Hilbert space and $\mathcal{B}(\mathcal{H})$ the algebra of all bounded linear operators on $\mathcal H$. The star partial order is defined by $A\overset{*}{\leq}B$ if and only if…
A continuous linear operator L defined on the space of entire functions H(C) is said to be an extended $lambda$-eigenoperator of the differentiation operator D provided DL = $lambda$LD. Here we fully characterize when an extended…
We present a generalization of the Clifford action for other representations spaces of $Spin(n)$, which is called the Clifford homomorphism. Their properties extend to the ones for the higher spin Dirac operators on spin manifolds. In…