Approximation by rational modules on boundary sets

Sets of exact approximation order by rational numbers III

For a function Ψ : R>0 → R>0, let Exact(Ψ) be the set of real numbers that are approximable by rational numbers to order Ψ, but to no order cΨ with 0 < c < 1. When Ψ is non-increasing and satisfies Ψ(x) = o(x−2), we establish that Exact(Ψ) has Hausdorff dimension 2/λ, where λ is the lower order at infinity of the function 1/Ψ. Furthermore, we study the set Exact(Ψ) when Ψ is not assumed to be n...

Homotopy approximation of modules

Deleanu, Frei, and Hilton have developed the notion of generalized Adams completion in a categorical context. In this paper, we have obtained the Postnikov-like approximation of a module, with the help of a suitable set of morphisms.

Approximation by Rational Functions

Approximation by Rational Functions

Making use of the Hardy-Littlewood maximal function, we give a new proof of the following theorem of Pekarski: If f' is in L log L on a finite interval, then f can be approximated in the uniform norm by rational functions of degree n to an error 0(1/n) on that interval. It is well known that approximation by rational functions of degree n can produce a dramatically smaller error than that for p...

A Note on Approximation by Rational Functions

The theory of the approximation by rational functions on point sets E of the js-plane (z = x+iy) has been summarized by J. L. Walsh who himself has proved a great number of important theorems some of which are fundamental. The results concern both the case when E is bounded and when E extends to infinity. In the present note a Z^-theory (0<p< oo) will be given for the following point sets exten...