Let π be a projective unitary representation of a countable group G on a separable Hilbert space H. If the set Bπ of Bessel vectors for π is dense in H, then for any vector x ∈ H the analysis operator Θx makes sense as a densely defined operator from Bπ to ` (G)-space. Two vectors x and y are called π-orthogonal if the range spaces of Θx and Θy are orthogonal, and they are π weakly equivalent i...

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...

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.

In This paper, we give a necessary condition for function in $L^2$ with its dual to generate a dual shearlet tight frame with respect to admissibility.

T he Meijer G–functions are a remarkable family G of functions of one variable, each of them determined by finitely many indices. Although each such function is a linear combination of certain special functions of standard type, they seem not to be well known in the mathematical community generally. Indeed they are not even mentioned in most books on special functions, e.g., [1], [18]. Even the...

Bessel processes with constant negative drift have recently appeared as heavy-traffic limits in queueing theory. We derive a closed-form expression for the spectral representation of the transition density of the Bessel process of order ν > −1 with constant drift μ = 0. When ν > − 1 2 and μ < 0, the first term of the spectral expansion is the steady-state gamma density corresponding to the zero...

G-frames are natural generalizations of frames which cover many other recent generalizations of frames, e.g., bounded quasi-projectors, frames of subspaces, outer frames, oblique frames, pseudo-frames and a class of timefrequency localization operators. Moreover, it was shown that g-frames are equivalent to stable space splittings. In this paper, we study the stability of g-frames. We first pre...