G V Badalian

(Author)

Quasipower Series and Quasianalytic Classes of FunctionsHardcover, 1 January 2002

Quasipower Series and Quasianalytic Classes of Functions
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Part of Series
Translations of Mathematical Monographs
Print Length
183 pages
Language
English
Publisher
American Mathematical Society(RI)
Date Published
1 Jan 2002
ISBN-10
0821829432
ISBN-13
9780821829431

Description

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.

Product Details

Book Format:
Hardcover
Date Published:
1 January 2002
ISBN-10:
0821829432
ISBN-13:
9780821829431
Language:
English
Pages:
183