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Finite speed of propagation and local boundary conditions for wave equations with point interactions. (English) Zbl 1113.47063
Summary: We show that the boundary conditions entering in the definition of the self-adjoint operator \(\Delta^{A,B}\) describing the Laplacian plus a finite number of point interactions are local if and only if the corresponding wave equation \(\ddot\phi=\Delta^{A,B}\phi\) has finite speed of propagation.

MSC:
47N50 Applications of operator theory in the physical sciences
35L05 Wave equation
35L10 Second-order hyperbolic equations
47B25 Linear symmetric and selfadjoint operators (unbounded)
81Q10 Selfadjoint operator theory in quantum theory, including spectral analysis
47A55 Perturbation theory of linear operators
81Q15 Perturbation theories for operators and differential equations in quantum theory
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