Class of differentiability
From Encyclopedia of Mathematics
smoothness class 
, 
A concept characterizing differentiable mappings (in particular, functions). The class 
consists of all continuous functions, the class 
consists of functions with continuous derivatives of all orders not exceeding 
(in particular, 
is the class of functions with continuous derivatives of all orders), and the class 
consists of all real-analytic functions.
Comments
The notation 
(
for analytic) is somewhat unusual. Instead one mostly uses 
(
denotes the first transfinite ordinal number).
How to Cite This Entry:
Class of differentiability. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Class_of_differentiability&oldid=16922
Class of differentiability. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Class_of_differentiability&oldid=16922
This article was adapted from an original article by M.I. Voitsekhovskii (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article