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Inverse spectral problem for analytic plane domains I: Balian-Bloch trace formula

Steve Zelditch
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Abstract

We give a rigorous version of the classical Balian-Bloch trace formula, a semiclassical expansion around a periodic reflecting ray of the (regularized) resolvent of the Dirichlet Laplacian on a bounded smooth plane domain. It is equivalent to the Poisson relation (or wave trace formula) between spectrum and closed geodesics. We view it primarily as a computational device for explicitly calculating wave trace invariants. Its effectiveness will be illustrated in subsquent articles in the series in which concrete inverse spectral results are proved.

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Steve Zelditch. 2003-04-08. Inverse spectral problem for analytic plane domains I: Balian-Bloch trace formula. https://doi.org/10.1007/s00220-004-1074-y

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