Document Zbl 0871.58080 - zbMATH Open
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Self-adjoint elliptic operators and manifold decompositions. I: Low eigenmodes and stretching. (English) Zbl 0871.58080
The authors study the behavior of analytic invariants for manifolds that can be split as the union of two submanifolds along a splitting submanifold \(\Sigma\). In this paper, they study the low eigensolutions of a self-adjoint elliptic operator using a splicing construction to get an approximated solution of the operator given \(L^2\) solutions on both sides with a common limiting eigenvalue. They discuss manifolds with cylindrical ends and the Mayer-Vietoris sequence in an appendix. They concentrate on first order self-adjoint operators of Atiyah-Patodi-Singer type near \(\Sigma\) and extend work of R. G. Douglas and K. P. Wojciechowski [Commun. Math. Phys. 142, No. 1, 139-168 (1991; Zbl 0746.58074)] regarding additivity of spectral invariants.
MSC:
| 58J50 | Spectral problems; spectral geometry; scattering theory on manifolds |