Resolvent expansions for self-adjoint operators via boundary triplets. (English) Zbl 1529.35312
The authors consider a densely defined closed symmetric operator with equal (possibly infinite) deficiency indexes acting in a complex Hilbert space. Then via a boundary triplet the authors consider a one parameter family of self-adjoint extensions of \(A\) that is associated to a \(C^2\) path of Lagrangian planes and compute second order Taylor expansions for the resolvents and eigenvalue curves of the operators of the one the parameter family of extensions around some appropriate value of the parameter. Next the authors consider a specific form of Lagrangian planes and derive explicit formulas for the first and second order derivatives of the eigenvalues of the extensions that bifurcate from possibly multiple eigenvalues. The authors also provide some explicit example.
Reviewer: Massimo Lanza de Cristoforis (Padova)
MSC:
| 35P05 | General topics in linear spectral theory for PDEs |
| 35B20 | Perturbations in context of PDEs |
| 47A55 | Perturbation theory of linear operators |
| 47A75 | Eigenvalue problems for linear operators |
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