| Popis: |
Suppose K is a compact convex subset of R n. If for every x∈ R n , the net of best lp-approximants, from K, of x converges to the strict uniform approximant as p → ∞, we call K a strict Polya set. Two conditions which guarantee that K is a strict Polya set have recently been published. The present paper shows that these conditions are essentially equivalent, demonstrates that all closed strictly convex sets satisfy the conditions, and describes a set which is strict Polya but does not satisfy the conditions. |
