Related papers: Linear spectral transformations of Carath\'eodory …
Spectral functions play a central role in the characterization of a wide range of physical systems, including strongly interacting quantum field theories and many-body systems. Their non-perturbative determination from Euclidean correlation…
Functional linear models are one of the most fundamental tools to assess the relation between two random variables of a functional or scalar nature. This contribution proposes a goodness-of-fit test for the functional linear model with…
The literature on time series of functional data has focused on processes of which the probabilistic law is either constant over time or constant up to its second-order structure. Especially for long stretches of data it is desirable to be…
The article investigates the possibility of measuring the strength of a linear correlation relationship between nominal data and numerical data. Correlation coefficients for variables coded with real numbers as well as for variables coded…
Quadratic Wiener functionals are investigated systematically through transformations of order one on the Wiener space with the help of Malliavin calculus. The bi-directional relationship between quadratic Wiener functionals and…
In this paper we study the behaviour at infinity of the Fourier transform of Radon measures supported by the images of fractal sets under an algorithmically random Brownian motion. We show that, under some computability conditions on these…
The simplest examples of chaotic maps are linear, area-preserving maps on the circle, torus, or product of tori; respectively known as the Bernoulli map, the cat map, and the recently introduced "spatiotemporal" cat map. We study…
The statistical properties of the quantum chaotic spectra have been studied, so far, only up to the second order correlation effects. The numerical as well as the analytical evidence that random matrix theory can successfully model the…
Despite being the most popular methods of data analysis, Fourier-based techniques suffer from the problem of static resolution that is currently believed to be a fundamental limitation of the Fourier Transform. Although alternative…
We consider a class of L\'evy-type processes on which spectral analysis technics can be made to produce optimal results, in particular for the decay rate of their survival probability and for the spectral gap of their ground state…
We develop a model to describe the motional (i.e., external degree of freedom) energy spectra of atoms trapped in a one-dimensional optical lattice, taking into account both axial and radial confinement relative to the lattice axis. Our…
There is a growing interest in methods for detecting and interpreting changes in experimental time evolution data. Based on measured time series, the quantitative characterization of dynamical phase transitions at bifurcation points of the…
Modular equations occur in number theory, but it is less known that such equations also occur in the study of deformation properties of quasiconformal mappings. The authors study two important plane quasiconformal distortion functions,…
We compute non-perturbative spectral functions in a scalar $\phi^4$-theory in three spacetime dimensions via the spectral functional renormalisation group. This approach allows for the direct, manifestly Lorentz covariant computation of…
A method is presented to obtain the change in the potential and in the relevant wavefunction of a linear system of ordinary differential equations containing a spectral parameter, when that linear system is perturbed and a finite number of…
Linear diffusions are used to model a large number of stochastic processes in physics, including small mechanical and electrical systems perturbed by thermal noise, as well as Brownian particles controlled by electrical and optical forces.…
In the framework of an extended phenomenological approach to phase transitions, it is shown that existing nonlinear relation between local critical atomic parameters and phenomenological order parameter induces the corresponding nonlinear…
The correlation spectroscopy has been successfully employed in the measurement of the intrinsic linewidth of electromagnetically induced transparency (EIT) in time and frequency domain. We study the role of the sidebands of the intense…
We consider the general form of the linear transformation for point rotation coordinate frames. The frames have the rotation axis at every point. In the transformation the frequency of one frame relative to another is not equivalent to the…
This survey mainly deals with the tilted Carath{\'e}odory class by angle $\lambda$ (denoted by $\mathcal{P}_{\lambda}$) an element of which maps the unit disc into the tilted right half-plane $\{w: \Re e^{i\lambda} w>0\}$. Firstly we will…