Scattering of waves by periodically moving bodies |
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Authors: | Jeffery Cooper Walter Strauss |
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Institution: | Department of Mathematics, University of Maryland, College Park, Maryland 20742 USA;Department of Mathematics, Brown University, Providence, Rhode Island 02912 USA |
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Abstract: | We consider solutions of the scalar wave equation vanishing on the boundary of an obstacle which undergoes periodic motion. In analogy with the Lax-Phillips theory, we show that the scattering matrix, as a function of frequency, is holomorphic in a lower half-plane, and meromorphic in an upper half-plane, provided rays are not trapped. The poles of the scattering matrix correspond to certain outgoing eigenfunctions, and there is a near-field expansion of finite energy solutions in terms of these eigenfunctions. |
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