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We present examples for the calculation of the distribution and fragmentation functions using the representation in terms of non-local matrix elements of quark field operators. As specific examples, we use a simple spectator model to…
This study focuses on statistical inference for the class of quasi-infinitely divisible (QID) distributions, which was recently introduced by Lindner, Pan and Sato (2018). The paper presents a Fourier approach, based on the analogue of the…
The Fourier transform of a bounded measurable function, $f$, on the real line is shown to be the second distributional derivative of a H\"older continuous function. The Fourier transform is written as the difference of $\int_{-1}^1…
Covariance functions and variograms play a fundamental role in exploratory analysis and statistical modelling of spatial and spatio-temporal datasets. In this paper, we construct a new class of spatial covariance functions using the Fourier…
One of the most prominent quasiprobability functions in quantum mechanics is the Wigner function that gives the right marginal probability functions if integrated over position or momentum. Here we depart from the definition of the…
Normalisation in probability theory turns a subdistribution into a proper distribution. It is a partial operation, since it is undefined for the zero subdistribution. This partiality makes it hard to reason equationally about normalisation.…
We provide an introduction of some basic facts of uniformly almost periodic functions, such as Fourier series representations. A result is then proved about Fourier coefficients which is a generalization of the purely periodic case. We then…
We present a new approach to semiparametric inference using corrected posterior distributions. The method allows us to leverage the adaptivity, regularization and predictive power of nonparametric Bayesian procedures to estimate…
The ability to represent complex high dimensional probability distributions in a compact form is one of the key insights in the field of graphical models. Factored representations are ubiquitous in machine learning and lead to major…
Based on the definition of the Fourier transform in terms of the number operator of the quantum harmonic oscillator and in the corresponding definition of the fractional Fourier transform, we have obtained the discrete fractional Fourier…
The essentials of fractional calculus according to different approaches that can be useful for our applications in the theory of probability and stochastic processes are established. In addition to this, from this fractional integral one…
The Fast Fourier Transform is extended to functions on finite graphs whose edges are identified with intervals of finite length. Spectral and pseudospectral methods are developed to solve a wide variety of time dependent partial…
We introduce three one-parameter semigroups of operators and determine their spectra. Two of them are fractional integrals associated with the Askey-Wilson operator. We also study these families as families of positive linear approximation…
We consider certain finite sets of circle-valued functions defined on intervals of real numbers and estimate how large the intervals must be for the values of these functions to be uniformly distributed in an approximate way. This is used…
Fractional equations have become the model of choice in several applications where heterogeneities at the microstructure result in anomalous diffusive behavior at the macroscale. In this work we introduce a new fractional operator…
We prove a function field analog of Weyl's classical theorem on equidistribution of polynomial sequences. Our result covers the case in which the degree of the polynomial is greater than or equal to the characteristic of the field, which is…
Fractional moments have been investigated by many authors to represent the density of univariate and bivariate random variables in different contexts. Fractional moments are indeed important when the density of the random variable has…
A new concept, called quasi-linear transfer functions (QLTF), which can be used to characterize the output frequency behaviour of nonlinear systems, is introduced based on the well-known Volterra series representation. By using the new…
In this work, we are interested by the $q$-Bessel Fourier transform with a new approach. Many important results of this $q$-integral transform are proved with a new constructive demonstrations and we establish in particular the associated…
We present a formalism that enables the analytic calculation of the interaction of a spin-half particle with a polychromatic electromagnetic field. This powerful new approach provides a clear physical picture even for cases with highly…