We measure a sign interlacing phenomenon for Bessel sequences (uk) in L2 spaces terms of the Kantorovich–Rubinstein mass moving norm ‖uk‖KR. Our main observation shows that, quantitatively, rate at which ‖uk‖KR→0 heavily depends on Bernstein–Kolmogorov widths compact set Lipschitz functions. In particular, it dimension space. also establish lower bound convergence norms ‖uk‖X→0 basis/frame any ...

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...

In this article, a family of continuous functions on the unit sphere $$S\subseteq {\mathbb {R}}^{3}$$ is considered as generalization spherical harmonics. The fractalized using linear and bounded operator sphere. Particular values scale vector in iterated function system (IFS) may yield classical We have shown that for different IFS, Bessel sequences, frames, Riesz bases can be established spac...

Discrete analogs of the Lebedev–Skalskaya transforms are introduced and investigated. It involves series integrals with respect to kernels Re Kα+in(x),Im Kα+in(x),x>0,n∈N,|α|<1, i is imaginary unit Kν(z) modified Bessel function. The corresponding inversion formulas for suitable functions sequences in terms these established when α=±1/2. case α=0 reduces Kontorovich–Lebedev transform.

Given a frame for a subspace W of a Hilbert space H, we consider a class of oblique dual frame sequences. These dual frame sequences are not constrained to lie in W . Our main focus is on shift-invariant frame sequences of the form {φ(· − k)}k∈Z in subspaces of L2(R); for such frame sequences we are able to characterize the set of shift-invariant oblique dual Bessel sequences. Given frame seque...

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.