Uniform approximation on ideals of multilinear mappings

Uniform Approximation of Abhyankar Valuation Ideals in Smooth Function Fields

Let R be an n-dimensional regular local domain essentially of finite type over a ground field k of characteristic zero, and let ν be a rank one valuation centered on R. Recall that this is equivalent to asking that ν be an R-valued valuation on the fraction field K of R, taking non-negative values on R and positive values on the maximal ideal m ⊆ R. A theorem of Zariski and Abhyankar states tha...

A Remark on Absolutely Summing Multilinear Mappings *

In this note we obtain new coincidence theorems for absolutely summing multilinear mappings between Banach spaces. We also prove that our results, in general, can not be improved.

On Constrained Uniform Approximation

Uniform liftings of continuous mappings

We investigate the question of when a continuous mapping between subspaces of nonstandard hulls has a uniform lifting. 2000 Mathematics Subject Classification 03H05, 54J05 (primary); 54C20, 54D20, 54D65 (secondary)

On uniform approximation by splines

for 0 ≤ r ≤ k − 1. In particular, dist (f, S π) = O(|π| ) for f ∈ C(I), or, more generally, for f ∈ C(I), such, that f (k−1) satisfies a Lipschitz condition, a result proved earlier by different means [2]. These results are shown to be true even if I is permitted to become infinite and some of the knots are permitted to coalesce. The argument is based on a “local” interpolation scheme Pπ by spl...