The fast Hankel transform (FHT) implemented with digital filters has been the algorithm of choice in EM geophysics for a few decades. However, other disciplines have predominantly relied on methods that break up the Hankel transform integral into a sum of partial integrals that are each evaluated with quadrature. The convergence of the partial sums is then accelerated through a nonlinear sequen...

Abstract: This paper presents a strategy to design bilinear discrete cosine transform (DCT) algorithms of prime lengths. We show that by using multiplicative groups of integers, one can identify and arrange the computation as a pair of convolutions. When the DCT length p is such that (p−1)/2 is odd, the computation uses two (p−1)/2 point cyclic convolutions. When (p − 1)/2 = 2q with m > 0 and q...

Let ii be a bounded symmetric domain in C with normalized 2 volume measure dV . Let P be the orthogonal projection from L (il, dV) 2 2 onto the Bergman space La(Q) of holomorphic functions in L (ii, dV). Let P be the orthogonal projection from L (ii, dV) onto the closed subspace of antiholomorphic functions in L (ii, dV). The "little" Hankel operator h, with symbol / is the operator from La(Ci)...

A class ξ of algebras of symmetric n × n matrices, related to Toeplitz-plus-Hankel structures and including the well-known algebra H diagonalized by the Hartley transform, is investigated. The algebras of ξ are then exploited in a general displacement decomposition of an arbitrary n× n matrix A. Any algebra of ξ is a 1-space, i.e., it is spanned by n matrices having as first rows the vectors of...

Abstract Integrable operators arise in random matrix theory, where they describe the asymptotic eigenvalue distribution of large self-adjoint random matrices from the generalized unitary ensembles. This paper considers discrete Tracy–Widom operators, and gives sufficient conditions for a discrete integrable operator to be the square of a Hankel matrix. Examples include the discrete Bessel kerne...

The near threshold expansion of generalized sunset-type (water melon) diagrams with arbitrary masses is constructed by using a configuration space technique. We present analytical expressions for the expansion of the spectral density near threshold and compare it with the exact expression obtained earlier using the method of the Hankel transform. We formulate a generalized threshold expansion w...