Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

Remote Access
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)


Ulam-Zahorski problem on free interpolation by smooth functions

Author: A. Olevskiĭ
Journal: Trans. Amer. Math. Soc. 342 (1994), 713-727
MSC: Primary 26A48; Secondary 26A51, 41A05
MathSciNet review: 1179399
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let f be a function belonging to $ {C^n}[0,1]$. Is it possible to find a smoother function $ g \in {C^{n + 1}}$ (or at least $ {C^{n + \varepsilon }}$) which has infinitely many points of contact of maximal order n with f (or at least arbitrarily many such points with fixed norm $ {\left\Vert g \right\Vert _{{C^{n + \varepsilon }}}}$)? It turns out that for n = 0 and 1 the answer is positive, but if $ n \geq 2$, it is negative. This gives a complete solution to the Ulam-Zahorski question on free interpolation on perfect sets.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 26A48, 26A51, 41A05

Retrieve articles in all journals with MSC: 26A48, 26A51, 41A05

Additional Information

PII: S 0002-9947(1994)1179399-9
Article copyright: © Copyright 1994 American Mathematical Society

Comments: Email Webmaster

© Copyright , American Mathematical Society
Contact Us · Sitemap · Privacy Statement

Connect with us Facebook Twitter Google+ LinkedIn Instagram RSS feeds Blogs YouTube Podcasts Wikipedia