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 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 smal...

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Bibliographic Details
Published in:Boletim da Sociedade Brasileira de Matemática 2011-03, Vol.42 (1), p.45-74
Main Authors: Marmi, Stefano, Sauzin, David
Format: Article
Language:English
Subjects:
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Theoretical
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Summary:We discuss the quasianalytic properties of various spaces of functions suit-able for one-dimensional small divisor problems. These spaces are formed of functions 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.
ISSN:1678-7544
1678-7714
DOI:10.1007/s00574-011-0003-x