Related papers: Spectral Measures on Locally Fields
We derive necessary conditions for localization of continuous frames in terms of generalized Beurling densities. As an important application we provide necessary density conditions for sampling and interpolation in a very large class of…
It is found that, in addition to the conventional ones, a local approach to the relativistic quantum field theories at both zero and finite density consistent with the violation of Bell like inequalities should contain, and provide…
We present an approach to measure theory using the theory of locales. This includes concrete constructions of measure algebras associated to Radon measures, such as the Lebesgue measure on $\mathbb{R}^n$, via Grothendieck topologies…
Structured light harnessing multiple degrees of freedom has become a powerful approach to use complex states of light in fundamental studies and applications. Here, we investigate the light field of an ultrafast laser beam with a…
Take an interval $[t, t+1]$ on the $x$-axis together with the same interval on the $y$-axis and let $\rho$ be the normalized one-dimensional Lebesgue measure on this set of two segments. Continuing the work done by Lai, Liu and Prince…
We develop tools to study arithmetically induced singular continuous spectrum in the neighborhood of the arithmetic transition in the hyperbolic regime. This leads to first transition-capturing upper bounds on packing and multifractal…
A relativistic quantum field theory is presented for finite density problems based on the principle of locality. It is found that, in addition to the conventional ones, a local approach to the relativistic quantum field theories at both…
We extend the existence of ghost measures beyond nonnegative primitive regular sequences to a large class of nonnegative real-valued regular sequences. In the general case, where the ghost measure is not unique, we show that they can be…
Elastic light scattering has been extensively used to study samples showing a non uniform refraction index on lengthscales from a fraction of a micrometer to a fraction of a millimeter. Typically, a wide laser beam is sent through the…
The propagation of a Bessel beam (or Bessel-X wave) is analyzed on the basis of a vectorial treatment. The electric and magnetic fields are obtained by considering a realistic situation able to generate that kind of scalar field.…
We analyze some properties of the measures in the dual of the space $BV$, by considering (signed) Radon measures satisfying a perimeter bound condition, which means that the absolute value of the measure of a set is controlled by the…
The spectral density of random graphs with topological constraints is analysed using the replica method. We consider graph ensembles featuring generalised degree-degree correlations, as well as those with a community structure. In each case…
Based on the measurement of quantum correlation functions, the quantum statistical properties of spectral measurements are studied for broadband radiation fields. The spectral filtering of light before its detection is compared with the…
In this paper we investigate the problems related to measures with a natural spectrum (equal to the closure of the set of the values of the Fourier-Stieltjes transform). Since it is known that the set of all such measures does not have a…
The angular power spectrum of a stationary random field on the sphere is estimated from the needlet coefficients of a single realization, observed with increasingly fine resolution. The estimator we consider is similar to the one recently…
We present a method to measure the spectral density of in-band optical transmission impairments without coherent electrical reception and digital signal processing at the receiver. We determine the method's accuracy by numerical simulations…
For every frame spectral measure $ \mu $, there exists a discrete measure $ \nu $ as a frame measure. Since if $ \mu $ is not a frame spectral measure, then there is not any general statement about the existence of frame measures $ \nu $…
In this paper, we consider the problem of approximating the spectral distribution for a class of random operators over sofic groups. For this purpose, we make use of the concept of locally and empirically converging measures defined by…
We establish high probability estimates on the eigenvalue locations of Brownian motion on the $N$-dimensional unitary group, as well as estimates on the number of eigenvalues lying in any interval on the unit circle. These estimates are…
A theoretical description of local absorption is proposed in order to investigate spectral variations on a length scale comparable with the extension of the relevant quantum states. A general formulation is derived within the density-matrix…