Jonathan Gantner
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View article: Universality property of the S-functional calculus, noncommuting matrix variables and Clifford operators
Universality property of the S-functional calculus, noncommuting matrix variables and Clifford operators Open
Spectral theory on the S-spectrum was born out of the need to give quaternionic quantum mechanics a precise mathematical foundation (Birkhoff and von Neumann [8] showed that a general set theoretic formulation of quantum mechanics can be r…
View article: An Introduction to Hyperholomorphic Spectral Theories and Fractional Powers of Vector Operators
An Introduction to Hyperholomorphic Spectral Theories and Fractional Powers of Vector Operators Open
The aim of this paper is to give an overview of the spectral theories associated with the notions of holomorphicity in dimension greater than one. A first natural extension is the theory of several complex variables whose Cauchy formula is…
View article: Operator Theory on One-Sided Quaternionic Linear Spaces: Intrinsic S-Functional Calculus and Spectral Operators
Operator Theory on One-Sided Quaternionic Linear Spaces: Intrinsic S-Functional Calculus and Spectral Operators Open
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 …
View article: Analysing the impact of retrofitting and new construction through probabilistic life cycle assessment. A method applied to the environmental-economic payoff value of an intervention case in the Albanian building sector
Analysing the impact of retrofitting and new construction through probabilistic life cycle assessment. A method applied to the environmental-economic payoff value of an intervention case in the Albanian building sector Open
The EU building stock is relatively old with 40% of it built before 1960. In Albania the building sector accounts for 26, 9% of final energy consumption, offering high energy saving potentials due to the great number of old residential bui…
View article: Step-by-step implementation of BIM-LCA: A case study analysis associating defined construction phases with their respective environmental impacts
Step-by-step implementation of BIM-LCA: A case study analysis associating defined construction phases with their respective environmental impacts Open
Building Information Modelling (BIM) supports construction processes by dealing with the variety and complexity of design in a single virtual model. The model may also be complemented by the static and energy performance of buildings. Faci…
View article: Evolution by Schrödinger equation of Aharonov–Berry superoscillations in centrifugal potential
Evolution by Schrödinger equation of Aharonov–Berry superoscillations in centrifugal potential Open
In recent years, we have investigated the evolution of superoscillations under Schrödinger equation with non-singular potentials. In all those cases, we have shown that superoscillations persist in time. In this paper, we investigate the c…
View article: Fractional powers of vector operators and fractional Fourier’s law in a Hilbert space
Fractional powers of vector operators and fractional Fourier’s law in a Hilbert space Open
In this paper we give a concrete application of the spectral theory based on\nthe notion of $S$-spectrum to fractional diffusion process. Precisely, we\nconsider the Fourier law for the propagation of the heat in non homogeneous\nmaterials…
View article: Operator Theory on One-Sided Quaternionic Linear Spaces: Intrinsic\n S-Functional Calculus and Spectral Operators
Operator Theory on One-Sided Quaternionic Linear Spaces: Intrinsic\n S-Functional Calculus and Spectral Operators Open
Two themes drive this article: identifying the structure necessary to\nformulate quaternionic operator theory and revealing the relation between\ncomplex and quaternionic operator theory.\n The theory of quaternionic right linear operators…
View article: An Application of the $S$-Functional Calculus of the $S$-Functional Calculus to Fractional Diffusion Processes
An Application of the $S$-Functional Calculus of the $S$-Functional Calculus to Fractional Diffusion Processes Open
In this paper we show how the spectral theory based on the notion of $S$-spectrum allows us to study new classes of fractional diffusion and of fractional evolution processes. We prove new results on the quaternionic version of the $H^\inf…
View article: Evolution of superoscillations for Schrödinger equation in a uniform magnetic field
Evolution of superoscillations for Schrödinger equation in a uniform magnetic field Open
Aharonov-Berry superoscillations are band-limited functions that oscillate faster than their fastest Fourier component. Superoscillations appear in several fields of science and technology, such as Aharonov’s weak measurement in quantum me…
View article: A direct approach to the $S$-functional calculus for closed operators
A direct approach to the $S$-functional calculus for closed operators Open
The $S$-functional calculus for slice hyperholomorphic functions generalizes the Riesz-Dunford-functional calculus for holomorphic functions to quaternionic linear operators and to $n$-tuples of noncommuting operators. For an unbounded clo…
View article: Fractional powers of quaternionic operators and Kato’s formula using slice hyperholomorphicity
Fractional powers of quaternionic operators and Kato’s formula using slice hyperholomorphicity Open
In this paper we introduce fractional powers of quaternionic operators. Their definition is based on the theory of slice-hyperholomorphic functions and on the $S$-resolvent operators of the quaternionic functional calculus. The integral re…
View article: Functions of the infinitesimal generator of a strongly continuous quaternionic group
Functions of the infinitesimal generator of a strongly continuous quaternionic group Open
The quaternionic analogue of the Riesz–Dunford functional calculus and the theory of semigroups and groups of linear quaternionic operators have recently been introduced and studied. In this paper, we suppose that [Formula: see text] is th…