TY - JOUR
T1 - Ulam-zahorski problem on free interpolation by smooth functions
AU - Olevskiĭ, A.
PY - 1994/4
Y1 - 1994/4
N2 - Let f be a function belonging to Cn[0, 1]. Is it possible to find a smoother function g ϵ Cn+1(or at least Cn+ε) which has infinitely many points of contact of maximal order n with f (or at least arbitrarily many such points with fixed norm g Cn+ε)? It turns out that for n = 0 and 1 the answer is positive, but if n ≥ 2, it is negative. This gives a complete solution to the Ulam-Zahorski question on free interpolation on perfect sets.
AB - Let f be a function belonging to Cn[0, 1]. Is it possible to find a smoother function g ϵ Cn+1(or at least Cn+ε) which has infinitely many points of contact of maximal order n with f (or at least arbitrarily many such points with fixed norm g Cn+ε)? It turns out that for n = 0 and 1 the answer is positive, but if n ≥ 2, it is negative. This gives a complete solution to the Ulam-Zahorski question on free interpolation on perfect sets.
UR - http://www.scopus.com/inward/record.url?scp=20144384005&partnerID=8YFLogxK
U2 - 10.1090/S0002-9947-1994-1179399-9
DO - 10.1090/S0002-9947-1994-1179399-9
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AN - SCOPUS:20144384005
SN - 0002-9947
VL - 342
SP - 713
EP - 727
JO - Transactions of the American Mathematical Society
JF - Transactions of the American Mathematical Society
IS - 2
ER -