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OverviewIn this book, 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. Originally published in Russian, this English translation contains additional materials that treat the problems of classification of infinitely-differentiable functions, conditions for absolute convergence of quasipower series in terms of the functions that generate them, and the possibility of representing analytic functions by quasipower series in non-circular domains. 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. Full Product DetailsAuthor: G.V. BadalyanPublisher: American Mathematical Society Imprint: American Mathematical Society Volume: No. 216 Weight: 0.583kg ISBN: 9780821829431ISBN 10: 0821829432 Pages: 183 Publication Date: 30 November 2002 Audience: College/higher education , Professional and scholarly , Undergraduate , Postgraduate, Research & Scholarly Format: Hardback Publisher's Status: Active Availability: Temporarily unavailable ![]() The supplier advises that this item is temporarily unavailable. It will be ordered for you and placed on backorder. Once it does come back in stock, we will ship it out to you. Table of ContentsQuasianalytic 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.ReviewsAuthor InformationTab Content 6Author Website:Countries AvailableAll regions |