As a follow-up of previous work the authors, this considers uniform global time-renormalization functions for gravitational N-body problem. It improves on estimates radii convergence obtained therein by using completely different technique, both solution to original equations and renormalized ones. The aforementioned technique which new are built upon is known as majorants allows an easy applic...

The purpose of this paper is to highlight some hidden Markovian structure the concave majorant Brownian motion. Several distributional identities are implied by joint law a standard one-dimensional motion B and its almost surely unique K on [0,∞). In particular, distribution 2Kt−Bt that R5(t), where R5 5-dimensional Bessel process with R5(0)=0. 2K−B shares number other properties R5, we conject...

We extend the isotonic analysis for the Wicksell’s problem to estimate a regression function, which is motivated by the problem of estimating dark matter distribution in Astronomy. The main result is a version of the Kiefer-Wolfowitz theorem comparing the empirical distribution to its least concave majorant, but with a convergence rate n −1 log n faster than n−2/3 log n. The main result is usef...

A real sequence {xk} is said to be (∗)-monotone with respect to a sequence {pk} and a positive integer σ if xk > 0 and (−1)∆(xk − pkxk−σ) ≥ 0 for n ≥ 0. This paper is concerned with the existence of (∗)-monotone solutions of a neutral difference equation. Existence criteria are derived by means of a comparison theorem and by establishing explicit existence criteria for positive and/or bounded s...

Denote by Ln the projection operator obtained by applying the Lagrange interpolation method, weighted by (1 − x), at the zeros of the Chebyshev polynomial of the second kind of degree n + 1. The norm ‖Ln‖ = max ‖f‖∞≤1 ‖Lnf‖∞, where ‖ · ‖∞ denotes the supremum norm on [−1, 1], is known to be asymptotically the same as the minimum possible norm over all choices of interpolation nodes for unweight...

The affine synthesis operator Sc = P j>0 P k∈Zd cj,kψj,k is shown to map the mixed-norm sequence space `(`) surjectively onto L(R), 1 ≤ p < ∞, under mild conditions on the synthesizer ψ ∈ L(R) (say, having a radially decreasing L majorant near infinity) and assuming R Rd ψ dx = 1. Here ψj,k(x) = | det aj |ψ(ajx− k), for some dilation matrices aj that expand. Therefore the standard norm on f ∈ L...