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Finite speed of propagation and local boundary conditions for wave equations with point interactions


Authors: Pavel Kurasov and Andrea Posilicano
Journal: Proc. Amer. Math. Soc. 133 (2005), 3071-3078
MSC (2000): Primary 47B25, 81Q10; Secondary 47A55, 47N50, 81Q15
DOI: https://doi.org/10.1090/S0002-9939-05-08063-9
Published electronically: April 25, 2005
MathSciNet review: 2159787
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Abstract | References | Similar Articles | Additional Information

Abstract: 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.


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Additional Information

Pavel Kurasov
Affiliation: Department of Mathematics, Lund Institute of Technology, P.O. Box 118, 22100 Lund, Sweden
Email: kurasov@maths.lth.se

Andrea Posilicano
Affiliation: Dipartimento di Scienze, Università dell’Insubria, I-22100 Como, Italy
Email: posilicano@uninsubria.it

DOI: https://doi.org/10.1090/S0002-9939-05-08063-9
Keywords: Point interactions, singular perturbations, locality, wave equation
Received by editor(s): June 4, 2004
Published electronically: April 25, 2005
Communicated by: David S. Tartakoff
Article copyright: © Copyright 2005 American Mathematical Society

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