 00237 Mohamed S. ElBialy
 Local Contractions of Banach Spaces
and Spectral Gap Conditions
(111K, LaTeX 2e)
May 19, 00

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Abstract. In this work we study the linearization problem for a $C^{k,1}, k\geq 1,$
contraction of a Banach space $E$ near a fixed point which satisfies
a spectral gap condition and a narrow band condition both of order $k$.
We also assume that the part of the spectrum in each band
satisfies a finite nonresonant condition of
order $k$ relative to itself together with the part that lies
in the larger bands.
We show that there is a $C^{k,\gb}$ linearization for sufficiently small
$\gb > 0$.
We give a precise estimate on $\gb$ in terms of the gap and
band conditions.
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