 00233 Abel Klein, Andrew Koines, Maximilian Seifert
 Generalized eigenfunctions for waves in
inhomogeneous media
(107K, Latex 2e)
May 18, 00

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Abstract. Many wave propagation phenomena in classical physics are governed by
equations that can be recast in Schr\"odinger form. In this approach
the classical wave equation (e.g., Maxwell's equations, acoustic equation,
elastic equation) is rewritten in Schr\"odinger form, leading to the
study of the spectral theory of its \emph{classical wave operator},
a selfadjoint, partial differential operator on a Hilbert space of
vectorvalued, square integrable functions. Physically interesting
inhomogeneous media give rise to nonsmooth coefficients. We construct
a generalized eigenfunction expansion for classical wave operators with
nonsmooth coefficients. Our construction yields polynomially bounded
generalized eigenfunctions, the set of generalized eigenvalues forming
a subset of the operator's spectrum with full spectral measure.
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