Vol. 3, No. 4, 2010

Download this article
Download this article. For screen
For printing
Recent Issues

Volume 7
Issue 3, 529–770
Issue 2, 267–527
Issue 1, 1–266

Volume 6, Issues 1–8

Volume 5, Issues 1–5

Volume 4, Issues 1–5

Volume 3, Issues 1–4

Volume 2, Issues 1–3

Volume 1, Issues 1–3

The Journal
Cover
About the Cover
Editorial Board
Editors’ Addresses
Editors’ Interests
About the Journal
Scientific Advantages
Submission Guidelines
Submission Form
Subscriptions
Editorial Login
Contacts
Author Index
To Appear
 
ISSN: 1948-206X (e-only)
ISSN: 2157-5045 (print)
Analytic continuation of the resolvent of the Laplacian and the dynamical zeta function

Vesselin Petkov and Luchezar Stoyanov

Vol. 3 (2010), No. 4, 427–489
Abstract

Let s0 < 0 be the abscissa of absolute convergence of the dynamical zeta function Z(s) for several disjoint strictly convex compact obstacles Ki RN, i = 1,0, κ0 3, and let

R χ(z) = χ(− ‘ΔD − z2)−1χ, χ ∈ C0∞(ℝN ),

be the cutoff resolvent of the Dirichlet Laplacian ‘ΔD in the closure of RN i=1κ0Ki. We prove that there exists σ1 < s0 such that the cutoff resolvent Rχ(z) has an analytic continuation for

Im z < − σ1, |Re z| ≥ J1 > 0.

Keywords
open billiard, periodic rays, zeta function
Mathematical Subject Classification 2000
Primary: 35P20, 35P25
Secondary: 37D50
Milestones
Received: 30 March 2009
Revised: 20 February 2010
Accepted: 10 March 2010
Published: 8 September 2010
Authors
Vesselin Petkov
Université Bordeaux I
Institut de Mathématiques de Bordeaux
351, Cours de la Libération
33405 Talence
France
http://www.math.u-bordeaux1.fr/~petkov
Luchezar Stoyanov
School of Mathematics and Statistics
University of Western Australia
Perth, WA 6009
Australia
http://school.maths.uwa.edu.au/~stoyanov