Some applications of adherent series
Lefkovits, Henry Curt
Doctor of Philosophy
The notion of "adherence", or "adherent series" has been created by Mandelbrojt and applied to a number of diverse problems, such as generalized quasianalyticity, the theory of closure of certain sequences of functions, unicity problems for generalized moment problems, etc. The theory of adherent series is a most valuable and fundamental concept that serves to show the allied nature of these varied problems and provides a method by which the relations between them can be explored. The present work represents on one hand an extension of some results of Mandelbrojt on composition theorems to a more specialized problem, and the application of composition theorems to the study of a new quasianalytic class of functions, and on the other hand, an application of the concept of adherent series to the problem of characterizing an analytic almost periodic function.