ANALYTIC CONTINUATION OF THE RESOLVENT OF THE LAPLACIAN AND THE DYNAMICAL ZETA FUNCTION

Let s(0) < 0 be the abscissa of absolute convergence of the dynamical zeta function Z(s) for several disjoint strictly convex compact obstacles K-i subset of R-N, i = 1; ... ; kappa(0), kappa(0) >= 3, and let R-x(z) = chi (-Delta(D) - z(2))(-1) chi, chi is an element of C-0(infinity) (R-N), be the cutoff resolvent of the Dirichlet Laplacian -Delta(D) in the closure of R-N\U-i=1(kappa 0) K-i. i D 1 Ki. We prove that there exists sigma(1) < s(0) such that the cutoff resolvent R chi (z) has an analytic continuation for Im z < -sigma(1) vertical bar Re z vertical bar >= J(1) > 0: