Let be the abscissa of absolute convergence of the dynamical zeta function for several disjoint strictly convex compact obstacles and let , be the cut-off resolvent of the Dirichlet Laplacian in . We prove that there exists such that is analytic for and the cut-off resolvent has an analytic continuation for .
Soit l'abscisse de convergence absolue de la fonciton zeta dynamique pour des obstacles compacts, disjoints et strictement convexes et soit , la résolvante tronquée du Laplacien de Dirichlet dans . On prouve qu'il existe tel que est analytique pour et la résolvante tronquée admet un prolongement analytique pour .
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@article{CRMATH_2007__345_10_567_0, author = {Petkov, Vesselin and Stoyanov, Latchezar}, title = {Analytic continuation of the resolvent of the {Laplacian} and the dynamical zeta function}, journal = {Comptes Rendus. Math\'ematique}, pages = {567--572}, publisher = {Elsevier}, volume = {345}, number = {10}, year = {2007}, doi = {10.1016/j.crma.2007.10.019}, language = {en}, url = {http://archive.numdam.org/articles/10.1016/j.crma.2007.10.019/} }
TY - JOUR AU - Petkov, Vesselin AU - Stoyanov, Latchezar TI - Analytic continuation of the resolvent of the Laplacian and the dynamical zeta function JO - Comptes Rendus. Mathématique PY - 2007 SP - 567 EP - 572 VL - 345 IS - 10 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.crma.2007.10.019/ DO - 10.1016/j.crma.2007.10.019 LA - en ID - CRMATH_2007__345_10_567_0 ER -
%0 Journal Article %A Petkov, Vesselin %A Stoyanov, Latchezar %T Analytic continuation of the resolvent of the Laplacian and the dynamical zeta function %J Comptes Rendus. Mathématique %D 2007 %P 567-572 %V 345 %N 10 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.crma.2007.10.019/ %R 10.1016/j.crma.2007.10.019 %G en %F CRMATH_2007__345_10_567_0
Petkov, Vesselin; Stoyanov, Latchezar. Analytic continuation of the resolvent of the Laplacian and the dynamical zeta function. Comptes Rendus. Mathématique, Volume 345 (2007) no. 10, pp. 567-572. doi : 10.1016/j.crma.2007.10.019. http://archive.numdam.org/articles/10.1016/j.crma.2007.10.019/
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