Buch, Englisch, Band 216, Format (B × H): 184 mm x 260 mm, Gewicht: 561 g
Buch, Englisch, Band 216, Format (B × H): 184 mm x 260 mm, Gewicht: 561 g
Reihe: Translations of Mathematical Monographs
ISBN: 978-0-8218-2943-1
Verlag: American Mathematical Society
In this text, G.V. Badalyan addresses the fundamental problems of the theory of infinitely-differentiable functions using the theory of functions of quasianalytic classes.
In this text, G.V. Badalyan addresses the fundamental problems of the theory of infinitely-differentiable functions using the theory of functions of quasianalytic classes. A certain class of functions $C$ on an interval is called quasianalytic if any function in $C$ is uniquely determined by the values of its derivatives at any point. The obvious question, then, is how to reconstruct such a function from the sequence of values of its derivatives at a certain point. In order to answer that question, Badalyan combines a study of expanding functions in generalized factorial series with a study of quasipower series. The theory of quasipower series and its application to the reconstruction problem are explained in detail in this research monograph. Along the way other, related problems are solved, such as Borel's hypothesis that no quasianalytic function can have all positive derivatives at a point.
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
