BOUNDARY QUASI-ANALYTICITY AND A PHRAGMEN-LINDELOF TYPE THEOREM IN CLASSES OF FUNCTIONS OF BOUNDED TYPE IN TUBULAR DOMAINS

A complete description is obtained of the Carleman classes on R such that every function of bounded type in C-+(n) whose boundary values belong to the class under study is in fact a member of the corresponding Carleman class in C-+(n )boolean OR R-n. Also a refinement of the classical Salinas theorem is obtained, namely: under the conditions of the Salinas theorem on quasi-analyticity, instead of the assumption that a function belongs to the Carleman class in C-+(n )boolean OR R-n it suffices that its boundary values on R-n belong to the Carleman class, and the function is of bounded type in C-+(n).