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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.
Bulletin of the Brazilian Mathematical Society, New Series – Springer Journals
Published: Feb 23, 2011
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