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Sjöstrand, Johannes; Zworski, Maciej

Elementary linear algebra for advanced spectral problems. (English) Zbl 1140.15009

Ann. Inst. Fourier 57, No. 7, 2095-2141 (2007).
The paper starts by presenting several simple examples, showing different ways of constructing Grushin problems. After reviewing basic linear algebra techniques which are useful when considering Grushin problems, the authors give the basic idea in the context of Grushin problems and use it to prove the Poisson summation formula. Four advanced examples, in which the Grushin problem appears exactly, are presented at the end of the paper.
Reviewer: Nicholas Karampetakis (Thessaloniki)

Cited in 45 Documents

MSC:

15A21 Canonical forms, reductions, classification
35P05 General topics in linear spectral theory for PDEs
35Q40 PDEs in connection with quantum mechanics
81Q15 Perturbation theories for operators and differential equations in quantum theory
47A10 Spectrum, resolvent

Keywords:

Grushin problem; Schur complement; feshback reduction; eigenvalues; resonances; trace formulae; Poisson summation formula
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References:

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