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Transplantation and isospectrality. I. (Transplantation et isospectralité. I.) (French) Zbl 0735.58008
This paper gives new combinatorial geometric proofs of Sunada’s theorem concerning isospectral manifolds (both for the eigenvalue spectrum and for the length spectrum). The proofs also apply to non-smooth metrics and to natural operators. The paper includes examples of non-isometric complete non-compact manifolds that are isospectral in the following sense: they have the same discrete part of the spectrum and their scattering matrices are unitarily conjugate (in this sense, one can say that these manifolds have the same continuous spectra).
Reviewer: P.Bérard

MSC:
58C40 Spectral theory; eigenvalue problems on manifolds
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References:
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