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A quasianalyticity property for monogenic solutions of small divisor problems

A quasianalyticity property for monogenic solutions of small divisor problems We discuss the quasianalytic properties of various spaces of functions suit-able for one-dimensional small divisor problems. These spaces are formed of functions [InlineMediaObject not available: see fulltext.]1-holomorphic on certain compact sets K j of the Riemann sphere (in the Whitney sense), as is the solution of a linear or non-linear small divisor problem when viewed as a function of the multiplier (the intersection of K j with the unit circle is defined by a Diophantine-type condition, so as to avoid the divergence caused by roots of unity). It turns out that a kind of generalized analytic continuation through the unit circle is possible under suitable conditions on the K j ’s. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Bulletin of the Brazilian Mathematical Society, New Series Springer Journals

A quasianalyticity property for monogenic solutions of small divisor problems

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References (34)

Publisher
Springer Journals
Copyright
Copyright © 2011 by Springer
Subject
Mathematics; Theoretical, Mathematical and Computational Physics; Mathematics, general
ISSN
1678-7544
eISSN
1678-7714
DOI
10.1007/s00574-011-0003-x
Publisher site
See Article on Publisher Site

Abstract

We discuss the quasianalytic properties of various spaces of functions suit-able for one-dimensional small divisor problems. These spaces are formed of functions [InlineMediaObject not available: see fulltext.]1-holomorphic on certain compact sets K j of the Riemann sphere (in the Whitney sense), as is the solution of a linear or non-linear small divisor problem when viewed as a function of the multiplier (the intersection of K j with the unit circle is defined by a Diophantine-type condition, so as to avoid the divergence caused by roots of unity). It turns out that a kind of generalized analytic continuation through the unit circle is possible under suitable conditions on the K j ’s.

Journal

Bulletin of the Brazilian Mathematical Society, New SeriesSpringer Journals

Published: Feb 23, 2011

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