By Amnon Neeman

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We conclude that T IntX η˜ 2 = eL (h ∗ P X )( η˜ ) 2 ˚ X \ ΣX ) ∩ P ˚ X . 27, holds for an open set of η˜ ∈ (R X X ˚ ˚ X . 5), it remains this relation holds for all η˜ ∈ (R \ Σ ) ∩ P X X X true for all η ∈ (R \ Σ ) ∩ P . 149 DYNAMICS, LAPLACE TRANSFORM AND SPECTRAL GEOMETRY Appendix A. 5. We will make use of the following lemma whose proof we leave to the reader. 1. Let N be a compact smooth manifold, possibly with boundary, and let K ⊆ N be a compact subset. Let L := N × ∂I ∪ K × I where I := [0, 1].

26. H. Whitney, Complex analytic varieties (Addison-Wesley, Reading, MA, 1972). 27. D. V. Widder, The Laplace transform, Princeton Mathematical Series 6 (Princeton University Press, Princeton, NJ, 1941).

Austin and P. J. Braam, ‘Morse–Bott theory and equivariant cohomology’, The Floer memorial volume, Progress in Mathematics 133 (Birkh¨a user, Basel, 1995) 123–183. 2. J. M. Bismut and W. Zhang, ‘An extension of a theorem by Cheeger and M¨ u ller’, Ast´erisque 205 (Soci´et´e Math´ematique de France, Paris, 1992). 3. D. Burghelea, L. Friedlander, T. Kappeler and P. McDonald, ‘Analytic and Reidemeister torsion for representations in ﬁnite type Hilbert modules’, Geom. Funct. Anal. 6 (1996) 751–859.