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C. Watari [12] obtained a simple characterization of Lipschitz classes on the dyadic group using the -modulus of continuity and the best approximation by Walsh polynomials. Onneweer and Weiyi [4] characterized homogeneous Besov spaces on locally compact Vilenkin groups, but there are still some gaps to be filled up. Our purpose is to give the characterization of Besov spaces by oscillations, atoms and others on the dyadic groups. As applications, we show a strong capacity inequality of the...
Using systematically a tricky idea of N.V. Krylov, we obtain general results on the rate of convergence of a certain class of monotone approximation schemes for stationary Hamilton-Jacobi-Bellman equations with variable coefficients. This result applies in particular to control schemes based on the dynamic programming principle and to finite difference schemes despite, here, we are not able to treat the most general case. General results have been obtained earlier by Krylov for finite difference...
Using systematically a tricky idea of N.V. Krylov, we obtain
general results on the rate of convergence of a certain class of
monotone approximation schemes for stationary
Hamilton-Jacobi-Bellman equations with variable coefficients.
This result applies in particular to control schemes based on the
dynamic programming principle and to finite difference schemes
despite, here, we are not able to treat the most general case.
General results have been obtained earlier by Krylov for
finite...
Considering the class of almost periodic functions integrable in the Stepanov sense we extend and generalize certain results of the first author, as well as of L. Leindler and P. Chandra.
The result of this article together with [1] and [4] gives a full quantitative description of a Fatou type property for functions from Hardy classes in the upper half plane.
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