Related papers: Tempered distributions with discrete support and s…
In this note, we study the convergence from the discrete to the continuous non-linear Fourier transform. Relations between spectral problems and questions in complex function theory provide a new approach to the study of scattering problems…
The Lorentz covariant tempered disributions with the supports in the product of the closed upper light cones are described.
The present paper presents two new approaches to Fourier series and spectral analysis of singular measures.
We prove that each discrete set in the Euclidean space that has bounded changes under every translation is a bounded perturbation of a square lattice, i.e., a uniformly spread set in the sense of Laszkovich. In particular, the support of…
The purpose of this paper is to explore some mixtures of Kies distributions -- discrete and continuous. The last ones are also known as compound distributions. Some conditions for convergence are established. We study the probabilistic…
Products between phase-type distributed random variables and any independent, positive and continuous random variable are studied. Their asymptotic properties are established, and an expectation-maximization algorithm for their effective…
Transition from discrete to continuous Fourier series is studied for the functions becoming singular in the transition. Conditions are specified when summing replacement by integration is inadmissible.
We introduce the discrete distribution of a Wiener process range. Rather than finding some basic distributional properties including hazard rate function, moments, Stress-strength parameter and order statistics of this distribution, this…
We discuss bilinear estimates of tempered distributions in the Fourier restriction spaces for the two-dimensional Sch\"odinger equation whose principal part is the d'Alembertian. We prove that the bilinear estimates hold if and only if the…
We propose a new integral based on Taylor measures, study its properties extensively, and we illustrate that it includes many concepts from mathematics as special cases. In particular, the new integral emerges as a generalization of the…
The theory of commutative monads on cartesian closed categories provides a framework where aspects of the theory of distributions and other extensive quantities can be formulated and some results proved. We make explicit a link between our…
Considering discrete models, the univariate framework has been studied in depth compared to the multivariate one. This paper first proposes two criteria to define a sensu stricto multivariate discrete distribution. It then introduces the…
In this paper we prove existence and pathwise uniqueness for a class of stochastic differential equations (with coefficients $\sigma_{ij},b_i$ and initial condition $y$ in the space of tempered distributions) that maybe viewed as a…
In the present article, the author uses Fourier theory of tempered distributions (generalized functions) in deriving a formula for Dirichlet-like integrals. The applied method is remarkably efficient and allows a solution in a few…
In some fields of applications of stable distributions, especially in economics, it appears, that data have distributions similar to stable in a large region, but do not have such heavy tails. Our aim in this note is to propose several…
Bivariate partial-sums discrete probability distributions are defined. The question of the existence of a limit distribution for iterated partial summations is solved for finite-support bivariate distributions which satisfy conditions under…
We analyze solvability of a special form of distributed order fractional differential equations within the space of tempered distributions supported by the positive half-line.
In this paper we introduce a new parametric distribution, the Mixed Tempered Stable. It has the same structure of the Normal Variance Mean Mixtures but the normality assumption leaves place to a semi-heavy tailed distribution. We show that,…
We define Schwartz functions, tempered functions and tempered distributions on (possibly singular) real algebraic varieties. We prove that all classical properties of these spaces, defined previously on affine spaces and on Nash manifolds,…
We discuss some of the mathematical properties of the fractional derivative defined by means of Fourier transforms. We first consider its action on the set of test functions $\Sc(\mathbb R)$, and then we extend it to its dual set,…