Department of Mathematics, California State University San Marcos, San Marcos, California 92096-0001
Abstract:
It is well known that a function whose restriction to every line in is real analytic must itself be real analytic. In this note we study whether this property of real analytic functions is also possessed by some other subclasses of functions. We prove that if is ultradifferentiable corresponding to a sequence on every line in some `uniform way', then is ultradifferentiable corresponding to the sequence