An algorithm is presented for the accurate evaluation of Hankel (or Bessel) transforms of algebraically related kernel functions, defined here as the non-Bessel function portion of the integrand, that is more widely applicable than the standard digital filter methods without enormous increases in computational burden. The algorithm performs the automatic integration of the product of the kernel...

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...

The class of natural exponential families (NEFs) distributions having power variance functions (NEF-PVFs) is huge (uncountable), with enormous applications in various fields. Based on a characterization property that holds for the cumulants members this class, we developed novel goodness-of-fit (gof) test testing whether given random sample fits fixed class. We derived asymptotic null distribut...

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.

We consider families of E0-semigroups continuously parametrized by a compact Hausdorff space, which are cocycle-equivalent to a given E0-semigroup β. When the gauge group of β is a Lie group, we establish a correspondence between such families and principal bundles whose structure group is the gauge group of β. Let H be a Hilbert space, which we will always assume to be separable and infinitedi...

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...