exists for each x, y ∈ S(E). In this case E is called smooth. The norm of E is said to be Fréchet differentiable if for each x ∈ S(E) the limit is attained uniformly for y ∈ S(E). The normofE is called uniformlyFréchet differentiable if the limit is attained uniformly for x, y ∈ S(E). It is well known that (uniform) Fréchet differentiability of the norm of E implies (uniform) Gâteaux differenti...

We present a sharp uniform-in-bandwidth functional limit law for the increments of the Kaplan-Meier empirical process based upon right-censored random data. We apply this result to obtain limit laws for nonparametric kernel estimators of local functionals of lifetime densities, which are uniform with respect to the choices of bandwidth and kernel. These are established in the framework of conve...

Let a(z) be a meromorphic function having in the disk |z| < R precisely λ poles. In this work for the (λ−1)th row of the Padé table of a(z) the set of uniform convergence is explicitly obtained. The present note is a supplement to the previous work of the author (J. Approx. Theory, 123(2003), 160-207). In the theory of uniform convergence of the Padé approximants the principal question is if th...

‎We provide a uniform estimate for the $L^1$-norm (over any interval of bounded length) of the logarithmic derivatives‎ ‎of global normalizing factors associated to intertwining operators for the following reductive groups over number fields‎: ‎inner forms of $operatorname{GL}(n)$; quasi-split classical groups and their similitude groups; the exceptional group $G_2$‎. ‎This estimate is a key in...

1. Some aspects of classical empirical process theory: uniform laws of large numbers, process convergence and uniform central limit theorems. 2. M-estimation. Asymptotic theory of consistency, rates of convergence and limiting distribution. 3. Non-asymptotic theory of penalized empirical risk minimization; nonasymptotic deviation inequalities for suprema of empirical processes, oracle inequalit...

We extend F.Pastjin's construction of uniform decomposable chains of finite rank to those of rank 'finite over a limit' and investigate infinite (length ω) products and unions of such chains. We derive an extension of Pastjin's characterisation to uniform decomposable chains of small transfinite rank (≤ ω + ω).

EVARIST GINÉ and DAVID M. MASON Department of Mathematics, University of Connecticut and Statistics Program, University of Delaware ABSTRACT. We apply recent results on local U–statistcs to obtain uniform in bandwidth consistency and central limit theorems for some commonly used estimators of integral functionals of density functions. key words: kernel density estimator, uniform in bandwidth, U...

The polynomial-trigonometric interpolation based on the Krylov approach for a smooth function given on [-1, 1] is defined on the union of m shifted each other uniform grids with the equal number of points. The asymptotic errors of the interpolation in both uniform and L2 metrics are investigated. It turned out that the corresponding errors can be minimized due to an optimal choice of the shift ...

We consider Toeplitz operators with symbols enjoying a uniform radial limit on Segal–Bargmann type spaces. We show that such an operator is compact if and only if the limiting function vanishes on the unit sphere. The structure of the C∗-algebra generated by Toeplitz operators whose symbols admit continuous uniform radial limits is also analyzed.

For a re-entrant line operating under the last-buffer–first-serve service policy, there have been two independent proofs of a heavy traffic limit theorem. The key to these proofs is to prove the uniform convergence of a critical fluid model. We give a new proof for the uniform convergence of the fluid model.