Related papers: Scaled global operators and Fueter variables on no…
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…
In this note, we want to investigate the question, given a projective algebraic scheme X/k and coherent sheaves F, E on X, when do global differential operators of order N greater than zero, between E and F exist. We investigate in…
Two themes drive this article: identifying the structure necessary to formulate quaternionic operator theory and revealing the relation between complex and quaternionic operator theory. The theory of quaternionic right linear operators is…
This paper is a continuation of the research of our previous work and considers quaternionic generalized Carath\'eodory functions and the related family of generalized positive functions. It is addressed to a wide audience which includes…
The theory of quaternionic operators has applications in several different fields such as quantum mechanics, fractional evolution problems, and quaternionic Schur analysis, just to name a few. The main difference between complex and…
We establish formulae for the asymptotic growth (with respect to the scaling dimension) of the number of operators in effective field theory, or equivalently the number of $S$-matrix elements, in arbitrary spacetime dimensions and with…
This paper introduce a fractional-fractal $\psi$-Fueter operator in the quaternionic context inspired in the concepts of proportional fractional derivative and Hausdorff derivative of a function with respect to a fractal measure. Moreover,…
Correlation functions of local operators in Quantum Field Theory (QFT) on hyperbolic space can be fully characterized by the set of QFT data $\lbrace \Delta_i,C_{ijk},b^{\hat{\mathcal{O}}}_j\rbrace$. These are the scaling dimensions of…
In this paper we extend the $H^\infty$ functional calculus to quaternionic operators and to $n$-tuples of noncommuting operators using the theory of slice hyperholomorphic functions and the associated functional calculus, called…
A multipartite system comprised of $n$ subsystems, each of which is described with `local variables' in ${\mathbb Z}(d)$ and with a $d$-dimensional Hilbert space $H(d)$, is considered. Local Fourier transforms in each subsystem are defined…
We introduce new classes of right quaternionic Hilbert spaces of Bargmann-Fock type $\mathcal{GB}_{m}^{2}(\mathbb{H})$, labeled by nonnegative integer $m$, generalizing the so-called slice hyperholomorphic Bargmann-Fock space introduced…
This paper deals with some special integral transforms of Bargmann-Fock type in the setting of quaternionic valued slice hyperholomorphic and Cauchy-Fueter regular functions. The construction is based on the well-known Fueter mapping…
A promising theory of quaternion-valued functions of one quaternionic variable, now called slice regular functions, has been introduced in 2006. The basic examples of slice regular functions are power series centered at 0 on their balls of…
The study of $\psi-$hyperholomorphic functions defined on domains in $\mathbb R^4$ with values in $\mathbb H$, namely null-solutions of the $\psi-$Fueter operator, is a topic which captured great interest in quaternionic analysis. This…
Numerous attempts have been made to replicate the success of complex-valued algebra in engineering and science to other hypercomplex domains such as quaternions, tessarines, biquaternions, and octonions. Perhaps, none have matched the…
The construction, in [AJN], of a pseudodifferential calculus analogous to the Weyl calculus, in an infinite dimensional setting, required the introduction of convenient classes of symbols. In this article, we proceed with the study of these…
Tnis paper deals with some special integral transforms in the setting of quaternionic valued slice polyanalytic functions. In particular, using the polyanalytic Fueter mappings it is possible to construct a new family of polynomials which…
For a bounded quaternionic operator $T$ on a right quaternionic Hilbert space $\mathcal{H}$ and $\varepsilon >0$, the pseudo $S$-spectrum of $T$ is defined as \begin{align*} \Lambda_{\varepsilon}^{S}(T) := \sigma_S (T) \bigcup \left \{ q…
We study the fixed point that controls the IR dynamics of QED in $d = 4 - 2\epsilon$. We derive the scaling dimensions of four-fermion and bilinear operators beyond leading order in $\epsilon$-expansion. For the four-fermion operators, this…
Using the complex Klein-Gordon field as a model, we quantize the quaternionic scalar field in the real Hilbert space. The lagrangian formulation has accordingly been obtained, as well as the hamiltonian formulation, and the energy and…