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Inverse spectral problem for analytic plane domains I: Balian-Bloch trace formula (2001)
| Content Provider | CiteSeerX |
|---|---|
| Author | Zelditch, Steve |
| Description | This is the first in a series of papers [Z3, Z4, Z5, Z6, Z7] on inverse spectral/resonance problems for analytic plane domains Ω. In this paper, we present a rigorous version of the Balian-Bloch trace formula [BB1, BB2]. It is an asymptotic formula for the trace TrRρ(k + iτ) of the regularized resolvent of the Dirichlet Laplacian of Ω as k → ∞ with τ> 0 held fixed. When the support of ˆρ contains the length Lγ of precisely one periodic reflecting ray γ, then the asymptotic expansion of TrRρ(k + iτ) is essentially the same as the wave trace expansion at γ. The raison d’etre for this approach to wave invariants is that they are explicitly computable. Applications of the trace formula will be given in the subsequent articles in this series. For instance, in [Z4, Z5] we will prove that analytic domains with one symmetry are determined by their Dirichlet spectra. Although we only present details in dimension 2, the Balian-Bloch approach works the same in all dimensions. |
| File Format | |
| Language | English |
| Publisher Date | 2001-01-01 |
| Publisher Department | DEPARTMENT OF MATHEMATICS, JOHNS HOPKINS UNIVERSITY |
| Access Restriction | Open |
| Subject Keyword | Balian-bloch Trace Formula Bb1 Dirichlet Laplacian Regularized Resolvent Inverse Spectral Resonance Problem Asymptotic Expansion Analytic Plane Domain Iv Dirichlet Spectrum Analytic Plane Domain Analytic Domain Wave Trace Expansion Trace Formula Raison Etre Paper Z3 Subsequent Article Asymptotic Formula Rigorous Version Trace Trr Inverse Spectral Problem Balian-bloch Approach |
| Content Type | Text |
| Resource Type | Article |
