Related papers: Reflections on the q-Fourier transform and the q-G…
This article outlines a novel interpretation of quantum theory: the Q-based interpretation. The core idea underlying this interpretation, recently suggested for quantum field theories by Drummond and Reid [2020], is to interpret the phase…
We evaluate an adaptive gaussian quadrature integration scheme that will be suitable for the numerical evaluation of generalized redistribution in frequency functions. The latter are indispensable ingredients for "full non-LTE" radiation…
We consider the integral and derivative operators of tempered fractional calculus, and examine their analytic properties. We discover connections with the classical Riemann-Liouville fractional calculus and demonstrate how the operators may…
Using a general $q$-series expansion, we derive some nontrivial $q$-formulas involving many infinite products. A multitude of Hecke--type series identities are derived. Some general formulas for sums of any number of squares are given. A…
The purpose of this paper is to define generalized twisted q-Bernoulli numbers by using p-adic q-integrals. Furthermore, we construct a q-analogue of the p-adic generalized twisted L-functions which interpolate generalized twisted…
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…
Some calculations of parton distributions from first principles only give access to a limited range of Fourier modes of the function to reconstruct. We present a physically motivated procedure to regularize the inverse integral problem…
It has long been agreed by academics that the inversion method is the method of choice for generating random variates, given the availability of the quantile function. However for several probability distributions arising in practice a…
We propose flexible Gaussian representations for conditional cumulative distribution functions and give a concave likelihood criterion for their estimation. Optimal representations satisfy the monotonicity property of conditional cumulative…
The problem of renormalization in perturbative quantum field theory (pQFT) can be described in a rigorous way through the theory of extension of distributions. In the framework of pQFT a certain type of distribution appears, given by…
The functions on a lattice generated by the integer degrees of $q^2$ are considered, 0<q<1. The $q^2$-translation operator is defined. The multiplicators and the $q^2$-convolutors are defined in the functional spaces which are dual with…
We prove an explicit formula for the Fourier transform of $f(u(t))$, given the Fourier transform of $f(t)$, assuming $f\in L^2(-\infty,\infty)$ and $u$ sufficiently well behaved. We illustrate its usefulness by calculating the Fourier…
As an extension to the Laplace and Sumudu transforms the classical Natural transform was proposed to solve certain fluid flow problems. In this paper, we investigate q-analogues of the q-Natural transform of some special functions. We…
On the one hand the Fermi-Dirac and Bose-Einstein functions have been extended in such a way that they are closely related to the Riemann and other zeta functions. On the other hand the Fourier transform representation of the gamma and…
This manuscript reviews theoretical results and applications related to quadratic forms in Gaussian random variables. It summarizes definitions, canonical representations, exact and approximate distributional results, numerical inversion…
This paper concerns diffraction-tomographic reconstruction of an object characterized by its scattering potential. We establish a rigorous generalization of the Fourier diffraction theorem in arbitrary dimension, giving a precise relation…
The present article is devoted to the description of further investigations of the author of this article. These investigations (in terms of various representations of real numbers) include the generalized Salem functions and…
In this work, we generalize previous results about the Fractionary Schr\"{o}dinger Equation within the formalism of the theory of Tempered Ultradistributions. Several examples of the use of this theory are given. In particular we evaluate…
This article presents a new class of generalized transmuted lifetime distributions which includes a large number of lifetime distributions as sub-family. Several important mathematical quantities such as density function, distribution…
A new method for approximating fractional derivatives of the Gaussian function and Dawson's integral are presented. Unlike previous approaches, which are dominantly based on some discretization of Riemann-Liouville integral using polynomial…