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Proofs that Fredholm determinants of transfer operators for hyperbolic flowsare entire can be extended to a large new class of multiplicative evolutionoperators. We construct such operators both for the Gutzwiller semi-classicalquantum mechanics and for classical thermodynamic formalism, and introduce anew functional determinant which is expected to be entire for Axiom A flows,and whose zeros coincide with the zeros of the Gutzwiler-Voros zeta function.Comment: 4 pages, Revtex + one PS figure attached to the end of the text cut  before you run revtex

Entire Fredholm determinants for evaluation of semiclassical and thermodynamical spectra