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arXiv · 0706.0138

A quasianalyticity property for monogenic solutions of small divisor problems

Stefano Marmi·David Sauzin
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Abstract

We discuss the quasianalytic properties of various spaces of functions suitable for one-dimensional small divisor problems. These spaces are formed of functions C^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.

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Stefano Marmi, David Sauzin. 2007-06-01. A quasianalyticity property for monogenic solutions of small divisor problems. https://doi.org/10.1007/s00574-011-0003-x

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