Mathematics – Spectral Theory
Scientific paper
2001-11-07
Annals of Mathematics 70 (1) (2009), 205-269
Mathematics
Spectral Theory
56 pages, 9 figures. To appear in the Annals of Math
Scientific paper
This is part of a series of papers on the inverse spectral problem for bounded analytic plane domains. Here, we use the trace formula established in the first paper (`Balian-Bloch trace formula') to explicitly calculate wave trace invariants associated to bouncing ball orbits and dihedral rays. We use these invariants to prove that simply connected bounded analytic plane domains with one symmetry (which reverses a bouncing ball orbit of fixed length L) are spectrally determined in this class.
Zelditch Steve
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