ULAM-ZAHORSKI PROBLEM ON FREE INTERPOLATION BY SMOOTH FUNCTIONS

Authors
OLEVSKII A
Citation
A. Olevskii, ULAM-ZAHORSKI PROBLEM ON FREE INTERPOLATION BY SMOOTH FUNCTIONS, Transactions of the American Mathematical Society, 342(2), 1994, pp. 713-727
Citations number
13
Categorie Soggetti
Mathematics, General",Mathematics
Journal title
Transactions of the American Mathematical Society → ACNP
ISSN journal
00029947
Volume
342
Issue
2
Year of publication
1994
Pages
713 - 727
Database
ISI
SICI code
0002-9947(1994)342:2<713:UPOFIB>2.0.ZU;2-0
Abstract
Let f be a function belonging to C(n)[0, 1]. Is it possible to find a smoother function g is-an-element-of c(n+1) (or at least C(n+epsilon) which has infinitely many points of contact of maximal order n with f (or at east arbitrarily many such points with fixed norm parallel-to g parallel-to C(n+epsilon)? It turns out that for n = 0 and 1 the answe r is positive, but if n greater-than-or-equal-to 2, it is negative. Th is gives a complete solution to the Ulam-Zahorski question on free int erpolation on perfect sets.