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

   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Linear superposition of smooth functions


Author: Robert Kaufman
Journal: Proc. Amer. Math. Soc. 46 (1974), 360-362
MSC: Primary 26A72; Secondary 46E15
MathSciNet review: 0352374
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We give a simple proof of the impossibility of representing an arbitrary continuous function as a superposition (1), when $ {F_1}, \cdots ,{F_N}$ are smooth mappings of $ {R^{n + 1}}$ to $ {R^n}$. The main tool is the Riemann-Lebesgue lemma.


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


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 26A72, 46E15

Retrieve articles in all journals with MSC: 26A72, 46E15


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1974-0352374-2
PII: S 0002-9939(1974)0352374-2
Keywords: Smooth functions, Kolmogorov superposition theorem, Baire category
Article copyright: © Copyright 1974 American Mathematical Society