Bressaud X.
Subshift on an infinite alphabet
(89K, LaTeX)
ABSTRACT. We study transfer operators over
general subshifts of sequences of an infinite
alphabet. We introduce a family of Banach spaces of functions satisfying
a regularity
condition and a deacreasing condition. Under some assumptions on the
transfer operator,
we prove its continuity and quasi-compactness on these spaces. Under
additional
assumptions - existence of a conformal measure and topological mixing -
we
prove that its peripheral spectrum is reduced to 1 and
that this eigenvalue is simple. We describe the consequences of these
results
in terms of existence and properties of invariant measures absolutely
continuous with respect to the conformal measure. We also give some
examples of contexts in
which this setting can be used - expansive maps of the interval,
statistical mechanics.