where Jν(x) is the Bessel function of the first kind of order ν [1], and =z denotes the imaginary part of z. An extensive table of integral transforms involving the Bessel functions in the kernels is collected in [6]. Since the integration in (2) is with respect to the order of the Bessel function, such a pair of integral transforms is called index transform. Details about many other index tran...

Contents 1 Introduction 2 2 The Dirichlet problem and the boundary trace 7 2. Abstract We study the boundary value problem with measures for (E1) −∆u + g(|∇u|) = 0 in a bounded domain Ω in R N , satisfying (E2) u = µ on ∂Ω and prove that if g ∈ L 1 (1, ∞; t −(2N +1)/N dt) is nondecreasing (E1)-(E2) can be solved with any positive bounded measure. When g(r) ≥ r q with q > 1 we prove that any pos...

We review and study a one-parameter functional transformation, denoted by (S)β∈R, which allow, in the case β < 0, to provide a path realization of bridges of the family of diffusion processes which enjoy the time inversion property. This family includes the Brownian motion, the family of Bessel processes with a positive dimension and their conservative h-transforms. By means of these transforma...

Abstract We compute the multiplicative constant in large gap asymptotics of Meijer- G point process. This process generalizes Bessel and appears at hard edge Cauchy–Laguerre multi-matrix models certain product random matrix ensembles.

Maximum likelihood (ML) estimation for the generalized asymmetric Laplace (GAL) distribution also known as Variance gamma using simplex direct search algorithms is investigated. In this paper, we use numerical direct search techniques for maximizing the log-likelihood to obtain ML estimators instead of using the traditional EM algorithm. The density function of the GAL is only continuous but no...

This paper proposes a method to reproduce the Head Related Transfer Function (HRTF) in the horizontal auditory scene. The method is based on a separable representation which consists of a Fourier Bessel series expansion for the spectral components and a conventional Fourier series expansion for the spatial dependence. The proposed representation can be used to predict HRTFs at any azimuth posit...

For convex continuous functions f, g defined respectively in neighborhoods of points x, y in a normed linear space, a formula for the distance between ∂f(x) and ∂g(y) in terms of f, g (i.e. without using the dual) is proved. Some corollaries, like a new characterization of the subdifferential of a continuous convex function at a point, are given. This, together with a theorem from [4], implies ...