Quasipower series and quasianalytic classes of functions

In this book, G.V. Badalyan addresses the fundamental problems of the theory of infinitely-differentiable functions using the theory of functions of quasianalytic classes. The quasipower series technique explained here provides the means to extend the previously known results and elucidates their nature in the most relevant manner. This method also allows for thorough investigation of numerous problems of the theory of functions of quasianalytic classes by graduate students and research mathematicians.

Quasianalytic classes of functions, Generalizations of the Taylor formula. Quasipower series, Functions of Carleman's classes: Expansion in quasipower series, Criteria for the possibility of expanding functions in quasipower and factorial series, Generalized completely monotone functions and the condition for absolute convergence of a quasipower series (in the basic interval), On the use of quasipower series for representation of analytic functions in non-circular domains, Some applications of quasipower series to the theory of functions of quasianalytic classes, Bibliography