Luzin's condition (N) and modulus of continuity

On genuine Lupac{s}-Beta operators and modulus of continuity

In the present article we discuss approximation properties of genuine Lupac{s}-Beta operators of  integral type. We establish quantitative asymptotic formulae and a direct estimate in terms of Ditzian-Totik modulus of continuity. Finally we mention  results on the weighted modulus of continuity for the genuine operators.

Modulus of continuity on parts of the boundary and solid modulus of continuity

Uniform Modulus of Continuity of Random Fields

A sufficient condition for the uniform modulus of continuity of a random field X = {X(t), t ∈ RN} is provided. The result is applicable to random fields with heavy-tailed distribution such as stable random fields. Running head: Uniform Modulus of Continuity of Random Fields 2000 AMS Classification numbers: 60G60, 60G52, 60G17, 60G18.

Regularizability of Ill-posed Problems and the Modulus of Continuity

The regularization of linear ill-posed problems is based on their conditional well-posedness when restricting the problem to certain classes of solutions. Given such class one may consider several related real-valued functions, which measure the well-posedness of the problem on such class. Among those functions the modulus of continuity is best studied. For solution classes which enjoy the addi...

The modulus of continuity of analytic functions and CR- geometry

1 Introduction Contour and solid modulus of continuity. The one-dimensional case There has been an extensive study of the relation between the " contour " and the " solid " moduli of continuity for analytic functions in planar domains, starting with the following beautiful result of Hardy and Littlewood. For a domain G in C n (n ≥ 1) we denote as usual by A(G) the algebra of analytic functions ...