When f ≡ 1, the f -norm is the total variation norm, which is denoted ‖μ‖TV. Assume that P is aperiodic positive Harris recurrent with stationary distribution π. Then the iterated kernels P(x, ·) converge to π. The rate of convergence of P(x, .) to π does not depend on the starting state x, but exact bounds may depend on x. Hence, it is of interest to obtain non uniform or quantitative bounds o...

In image reconstruction and restoration, there exists an inherent tradeoff between the recovered spatial resolution and statistical variance: lower variance can be bought at the price of decreased spatial resolution. This tradeoff can be captured for a particular regularized estimator by tracing out the resolution and variance as a curve indexed by the estimator’s smoothing parameter. When the ...

This paper develops a multilevel least-squares approach for the numerical solution of the complex scalar exterior Helmholtz equation. This second-order equation is first recast into an equivalent first-order system by introducing several “field” variables. A combination of scaled L and H norms is then applied to the residual of this system to create a least-squares functional. It is shown that,...

A numerical method for a singular perturbation problem with a turning point is considered. The method uses non-equidistant discretization meshes. The first order accuracy, uniform in the perturbation parameter is proved in the discrete L1 norm.

Here we derive a multivariate fractional representation formula involving ordinary partial derivatives of …rst order. Then we prove a related multivariate fractional Ostrowski type inequality with respect to uniform norm. 2010 AMS Mathematics Subject Classi…cation : 26A33, 26D10, 26D15.

Here we derive multivariate weighted fractional representation formulae involving ordinary partial derivatives of …rst order. Then we present related multivariate weighted fractional Ostrowski type inequalities with respect to uniform norm. 2010 AMS Mathematics Subject Classi…cation : 26A33, 26D10, 26D15.

<p style='text-indent:20px;'>We address the Mach limit problem for Euler equations in an exterior domain with analytic boundary. We first prove existence of tangential vector fields constant analyticity radii and introduce norm which we distinguish derivatives taken from different directions. Then uniform boundedness solutions space on a time interval independent number, holds norm. The r...

The authors study the Hilbert Transform on the real line. They introduce some polynomial approximations and some algorithms for its numerical evaluation. Error estimates in uniform norm are given.

This paper solves two problems raised in [HSK]. The first is a uniform norm time-varying linear estimation problem and the second is a general time-varying linear control problem.

We consider two-dimensional quasilinear wave equations with standard null-type quadratic nonlinearities. In 2001 Alinhac proved that such systems possess global in time solutions for compactly supported initial data sufficiently small Sobolev norm. The highest norm of the constructed solution grows polynomially time. this work we develop a new strategy and prove uniform boundedness order all