Related papers: Discrete Bessel functions and transform
Bayesian solution of an inverse problem for indirect measurement $M = AU + {\mathcal{E}}$ is considered, where $U$ is a function on a domain of $R^d$. Here $A$ is a smoothing linear operator and $ {\mathcal{E}}$ is Gaussian white noise. The…
A new analytical approximation function is proposed to accurately fit the solution of a fractional differential equation of order one-half, whose nonhomogeneous term is defined by a modified Bessel function of the first kind. The exact…
A one to one correspondence between regular generalized bent functions from $\F_2^n$ to $\Z_{2^m},$ and $m-$tuples of Boolean bent functions is established. This correspondence maps self-dual (resp. anti-self-dual) generalized bent…
This article provides a novel and simple range description for the spherical mean transform of functions supported in the unit ball of an odd dimensional Euclidean space. The new description comprises a set of symmetry relations between the…
The decomposition of the tensor product of a positive and a negative discrete series representation of the Lie algebra su(1,1) is a direct integral over the principal unitary series representations. In the decomposition discrete terms can…
Fast Fourier transform was included in the Top 10 Algorithms of 20th Century by Computing in Science & Engineering. In this paper, we provide a new simple derivation of both the discrete Fourier transform and fast Fourier transform by means…
We consider sums of oscillating functions on intervals in cyclic groups of size close to the square root of the size of the group. We first prove non-trivial estimates for intervals of length slightly larger than this square root (bridging…
Signal scaling is a fundamental operation of practical importance in which a signal is enlarged or shrunk in the coordinate direction(s). Scaling or magnification is not trivial for signals of a discrete variable since the signal values may…
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…
Considering the kernel of an integral operator intertwining two realizations of the group of motions of the pseudo-Euclidian space, we derive two formulas for series containing Whittaker's functions or Weber's parabolic cylinder functions.…
We introduce a fractional Bessel process with constant negative drift, defined as a time-changed Bessel process via the inverse of a stable subordinator, independent of the base process. This construction yields a model capable of capturing…
We study $K$-types of degenerate principal series of ${\rm Sp}(n,\mathbb{C})$ by using two realisations of these infinite-dimensional representations. The first model we use is the classical compact picture; the second model is conjugate to…
A new representation for a regular solution of the perturbed Bessel equation of the form $Lu=-u"+\left( \frac{l(l+1)}{x^2}+q(x)\right)u=\omega^2u$ is obtained. The solution is represented as a Neumann series of Bessel functions uniformly…
We present an iterative method to obtain approximations to Bessel functions of the first kind $J_p(x)$ ($p>-1$) via the repeated application of an integral operator to an initial seed function $f_0(x)$. The class of seed functions $f_0(x)$…
We present a unified algebraic framework utilizing the formal Bell transform to bridge the Dirichlet convolution of arithmetic functions with the combinatorial structure of infinite Euler-type products. By analyzing the logarithmic…
In this paper we derive martingale estimating functions for the dimensionality parameter of a Bessel process based on the eigenfunctions of the diffusion operator. Since a Bessel process is non-ergodic and the theory of martingale…
We study correlation bounds under pairwise independent distributions for functions with no large Fourier coefficients. Functions in which all Fourier coefficients are bounded by $\delta$ are called $\delta$-{\em uniform}. The search for…
Beta regression has been extensively used by statisticians and practitioners to model bounded continuous data and there is no strong and similar competitor having its main features. A class of normalized inverse-Gaussian (N-IG) process was…
We investigate some fundamental properties of a peculiar class of special functions strictly related to Bessel, Anger and Weber functions, whose introduction was originally motivated by linear susceptibility tensor calculations in a hot,…
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…