Explicit eigenvalue estimates for transfer operators

Details Explicit eigenvalue estimates for transfer operators Explicit eigenvalue estimates for transfer operators

2008-02-12

arxiv.org/abs/0802.1638v1

Mathematics

Dynamical Systems

19 pages, to appear in Advances in Mathematics

Scientific paper

We consider transfer operators acting on spaces of holomorphic functions, and
provide explicit bounds for their eigenvalues. More precisely, if D is any open
set in C^d, and L is a suitable transfer operator acting on Bergman space
A^2(D), its eigenvalue sequence lambda_n(L) is bounded by |lambda_n(L)| \leq
A\exp(-a n^{1/d}), where a, A are explicitly given.

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