Related papers: A note on the Voigt profile function
We consider the problem of estimating convex boundaries from blurred and noisy observations. In our model, the convolution of an intensity function $f$ is observed with additive Gaussian white noise. The function $f$ is assumed to have…
We apply the Mellin-Barnes integral representation to several situations of interest in mathematical-physics. At the purely mathematical level, we derive useful asymptotic expansions of different zeta-functions and partition functions.…
In this note, we characterize the limiting functions in mod-Gausssian convergence; our approach sheds a new light on the nature of mod-Gaussian convergence as well. Our results in fact more generally apply to mod-* convergence, where *…
The Bargmann-Fock space(or Fock space for short) is a fundamental example of reproducing kernel Hilbert spaces that has found fascinating applications across multiple fields of current interest, including quantum mechanics, time-frequency…
This paper is mostly a survey, with a few new results. The first part deals with functional equations for q-exponentials, q-binomials and q-logarithms in q-commuting variables and more generally under q-Heisenberg relations. The second part…
Classical density functional theory (DFT) is a statistical mechanical theory for calculating the density profiles of the molecules in a liquid. It is widely used, for example. to calculate the density distribution of the molecules in the…
We describe a general framework of functional and Fourier analysis on domains with a free action of an Abelian Lie group $G$. Namely, on a domain of the form $G\times Y$ we introduce the appropriate spaces of distributions and measurable…
In this paper we find fractional Riemann-Liouville derivatives for the Takagi-Landsberg functions. Moreover, we introduce their generalizations called weighted Takagi-Landsberg functions which have arbitrary bounded coefficients in the…
Recently, there emerges different versions of beta function and hypergeometric functions containing extra parameters. Gaining enlightenment from these ideas, we will first introduce a new extension of generalized hypergeometric function and…
We study the distributions of values of the logarithmic derivatives of the Dedekind zeta functions on a fixed vertical line. The main object is determining and investigating the density functions of such value-distributions for any…
The advent of the Hohenberg-Kohn theorem in 1964, its extension to finite-T, Kohn-Sham theory, and relativistic extensions provide the well-established formalism of density-functional theory (DFT). This theory enables the calculation of all…
Flexion is a non-linear gravitational lensing effect that arises from gradients in the convergence and shear across an image. We derive a formalism that describes non-linear gravitational lensing by a circularly symmetric lens in the…
The functional-renormalization-group aided density-functional theory (FRG-DFT) is applied to the two-dimensional homogeneous electron gas (2DHEG). The correlation energy of the 2DHEG is derived as a function of the Wigner-Seitz radius $…
When dealing with highly accurate modeling of time and frequency transfers into arbitrarily moving dielectrics medium, it may be convenient to work with Gordon's optical spacetime metric rather than the usual physical spacetime metric.…
The imaging performance of tomographic deconvolution phase microscopy can be described in terms of the phase optical transfer function (POTF) which, in turn, depends on the illumination profile. To facilitate the optimization of the…
Using Gabor analysis, we give a complete characterization of all lattice sampling and interpolating sequences in the Fock space of polyanalytic functions, displaying a "Nyquist rate" which increases with $n$, the degree of polyanaliticity…
Considering the relationship between two bases in representation space of the three-dimensional proper Lorentz group, we derive some formulas with integrals involving Coulomb wave functions, which can be considered as Fourier, Mellin,…
In this paper density functionals for Coulomb systems subjected to electric and magnetic fields are developed. The density functionals depend on the particle density, $\rho$, and paramagnetic current density, $j^p$. This approach is…
We examine a family ${}_pG_{q}^{\mathbb C}\big[\genfrac{}{}{0pt}{}{(a)}{(b)};z\big]$ of integrals of Mellin-Barnes type over the space ${\mathbb Z}\times {\mathbb R}$, such functions $G$ naturally arise in representation theory of the…
This note presents a rigorous introduction to a selection of distributions along with their Fourier transforms, which are commonly encountered in signal processing and, in particular, magnetic resonance imaging (MRI). In contrast to many…