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Quasipower Series and Quasianalytic Classes of Functions
     

Quasipower Series and Quasianalytic Classes of Functions

by G. V. Badalyan
 

ISBN-10: 0821829432

ISBN-13: 9780821829431

Pub. Date: 12/28/2002

Publisher: American Mathematical Society

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

Overview

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. While the treatment is technical, the theory is developed chapter by chapter in detail, and the first chapter is of an introductory nature. 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.

Product Details

ISBN-13:
9780821829431
Publisher:
American Mathematical Society
Publication date:
12/28/2002
Series:
Translations of Mathematical Monographs , #216
Pages:
183

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