660 research outputs found
Quaternionic closed operators, fractional powers and fractional diffusion processes
No full textThis book presents a new theory for evolution operators and a new method for defining fractional powers of vector operators. This new approach allows to define new classes of fractional diffusion and evolution problems. These innovative methods and techniques, based on the concept of S-spectrum, can inspire researchers from various areas of operator theory and PDEs to explore new research directions in their fields. This monograph is the natural continuation of the book: Spectral Theory on the S-Spectrum for Quaternionic Operators by Fabrizio Colombo, Jonathan Gantner, and David P. Kimsey (Operator Theory: Advances and Applications, Vol. 270)
Including Route Choice Models into Pedestrian Movement Simulation Models
No full textBauer D, Gantner J. Including Route Choice Models into Pedestrian Movement Simulation Models. In: Pedestrian and Evacuation Dynamics 2012. Springer International Publishing; 2014: 713-727
Pflanzenökologische Untersuchungen in den subalpinen Dornpolsterfluren Kretas
No full textHager J. Pflanzenökologische Untersuchungen in den subalpinen Dornpolsterfluren Kretas. Dissertationes botanicae ; 89. Vaduz: Cramer in der Gantner-Verl.-Kommanditges.; 1985
An Introduction to Hyperholomorphic Spectral Theories and Fractional Powers of Vector Operators
No full textThe 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 used to define the holomorphic functional calculus for n-tuples of operators (A1, ... , An). A second way is to consider hyperholomorphic functions of quaternionic or paravector variables. In this case, by the Fueter-Sce-Qian mapping theorem, we have two different notions of hyperholomorphic functions that are called slice hyperholomorphic functions and monogenic functions. Slice hyperholomorphic functions generate the spectral theory based on the S-spectrum while monogenic functions induce the spectral theory based on the monogenic spectrum. There is also an interesting relation between the two hyperholomorphic spectral theories via the F-functional calculus. The two hyperholomorphic spectral theories have different and complementary applications. We finally discuss how to define the fractional Fourier’s law for nonhomogeneous materials using the spectral theory on the S-spectrum
Evolution by Schrödinger equation of Aharonov-Berry superoscillations in centrifugal potential
No full textIn 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 centrifugal potential, which is a singular potential, and we show that the techniques developed to study the evolution of superoscillations in the case of the Schrödinger equation with a quadratic Hamiltonian apply to this setting. We also specify, in the case of the centrifugal potential, the notion of super-shift of the limit solution, a fact explained in the last section of this paper. It then becomes apparent that superoscillations are just a particular case of super-shift
An introduction to fractional powers of quaternionic operators and new fractional diffusion processes
No full textEvolution of superoscillations for Schrödinger equation in a uniform magnetic field
No full textAharonov-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 mechanics, in optics, and in signal processing. An important issue is the study of the evolution of superoscillations using the Schrodinger equation when the initial datum is a weak value. Some superoscillatory functions are not square integrable, but they are real analytic functions that can be extended to entire holomorphic functions. This fact leads to the study of the continuity of a class of convolution operators acting on suitable spaces of entire functions with growth conditions. In this paper, we study the evolution of a superoscillatory initial datum in a uniform magnetic field. Moreover, we collect some results on convolution operators that appear in the theory of superoscillatory functions using a direct approach that allows the convolution operators to have non-constant coefficients of polynomial type
IGABEM2D
No full textThis MATLAB library implements adaptive isogeometric boundary element methods in 2D for the weakly-singular integral equation and the hyper-singular integral equation. Practical and theoretical details on the implementation are found in the accompanying paper [Gantner, Praetorius, Schimanko, Stable implementation of adaptive IGABEM in 2D in MATLAB, 2022]
Berezin transform of slice functions
No full textIn a recent paper, we introduced the Berezin transform of quaternionic linear operators and we obtained some properties in the setting of weighted Bergman spaces of slice hyperholomorphic functions. Here, we define the Berezin transform of slice functions, which corresponds to the case of a multiplication operator by certain quaternion-valued slice functions
- …
