We study Hilbert space aspects of the Klein-Gordon equation in two-dimensional spacetime. We associate to its restriction to a spacelike wedge a scattering from the past light cone to the future light cone, which is then shown to be (essentially) the Hankel transform of order zero. We apply this to give a novel proof, solely based on the causality of this spatio-temporal wave propagation, of th...

count ternary trees and the number of certain plane partitions and alternating sign matrices. Tamm evaluated these determinants by showing that the generating function for these entries has a continued fraction that is a special case of Gauss’s continued fraction for a quotient of hypergeometric series. We give a systematic application of the continued fraction method to a number of similar Han...

In this note we explore the properties of a simply defined family of Riordan arrays [9]. The inverses of these arrays are closely related to well-known Catalan-defined matrices. This motivates us to study the Hankel transforms [6] of the images of some well-known families of sequences under the inverse matrices. This follows a general principle which states that the Hankel transform of the imag...

We derive e cient approaches for two-parameter Hankel transforms. Such transforms arise, for example, in covariance matrix computations for performance modeling and evaluation of adaptive optics (AO) systems. Fast transforms are highly desirable since the parameter space for performance evaluation and optimization is large. They may be also applicable in real-time control algorithms for future ...

The Hankel transform is widely used to solve various engineering and physics problems, such as the representation of electromagnetic field components in medium, dynamic stress intensity factors, vibration axisymmetric infinite membrane displacement factors which all involve this type integration. However, traditional numerical integration algorithms cannot be due high oscillation characteristic...

whenever Φ is such that this extends to a bounded operator on Lpr0, asq. Whenever a is of no importance we will omit it from the notation. We abbreviate by saying that WΦ is a TWH-operator. These operators (or rather, unitarily equivalent ones) also go under the name finite interval convolution operators, truncated Hankel operators or Toeplitz operators on the Paley-Wiener space. See e.g. [1, 2...

The acoustic field is obtained in terms of the wave number integration for a horizontally stratified ocean. The Inverse Hankel Transform is obtained for shallow water over a Layered inhomogeneous elastic bottom using “Direct global Matrix approach” with Fast Field Approximation Technique. This paper presents the determination of total solution for the depth dependence of the field: the depth de...