Geodesic
Inverse spectral problem for analytic domains, II: $\mathbb Z_2$-symmetric domains
Steve Zelditch1
1 Department of Mathematics<br/>Johns Hopkins University<br/>Baltimore, MD 21218<br/>United States
Annals of mathematics, Tome 170 (2009) no. 1, pp. 205-269.

Voir la notice de l'article provenant de la source Annals of Mathematics website

This paper develops and implements a new algorithm for calculating wave trace invariants of a bounded plane domain around a periodic billiard orbit. The algorithm is based on a new expression for the localized wave trace as a special multiple oscillatory integral over the boundary, and on a Feynman diagrammatic analysis of the stationary phase expansion of the oscillatory integral. The algorithm is particularly effective for Euclidean plane domains possessing a $\mathbb{Z}_2$ symmetry which reverses the orientation of a bouncing ball orbit. It is also very effective for domains with dihedral symmetries. For simply connected analytic Euclidean plane domains in either symmetry class, we prove that the domain is determined within the class by either its Dirichlet or Neumann spectrum. This improves and generalizes the best prior inverse result that simply connected analytic plane domains with two symmetries are spectrally determined within that class.
DOI : 10.4007/annals.2009.170.205

Steve Zelditch 1

1 Department of Mathematics<br/>Johns Hopkins University<br/>Baltimore, MD 21218<br/>United States 
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Steve Zelditch. Inverse spectral problem for analytic domains, II: $\mathbb Z_2$-symmetric domains. Annals of mathematics, Tome 170 (2009) no. 1, pp. 205-269. doi : 10.4007/annals.2009.170.205. http://geodesic.mathdoc.fr/articles/10.4007/annals.2009.170.205/

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