Abstract. If $\{M_{k}\} _{k=0}^{\infty }$ is a logarithmically convex sequence of positive real numbers such that for all $k,$ $\rho ^{-k}M_{k}\leq M_{k+1}\leq\rho ^{-k}M_{k}$ for some $\rho >1,$ then it is proved that a function $f$ of $n$ real variables which is separately ultradifferentiable, with an additional ambient hypothesis, of class $C\{M_{k}\} $ in each variable is necessarily jointly ultradifferentiable of class $C\{M_{k}\} $.
AMS Subject Classification
(1991): 30D60, 46F05
Keyword(s):
Ultradifferentiable functions,
real analytic,
quasi-analytic,
separate analyticity
Received December 23, 1997. (Registered under 3303/2009.)
|