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Generalized eigenfunctions for waves in inhomogeneous media. (English) Zbl 1043.35097
This paper is devoted to the study of generalized eigenfunctions of classical wave operators with nonsmooth coefficients. Note that physically interesting inhomogeneous media give rise to nonsmooth coefficients in the classical wave equations, and hence in their classical wave operators. The authors construct a generalized eigenfunction expansion for classical wave operators which yields polynomially bounded generalized eigenfunctions, the set of generalized eigenvalues forming a subset of the operator’s spectrum with full spectral measure.

MSC:
35L05 Wave equation
35P10 Completeness of eigenfunctions and eigenfunction expansions in context of PDEs
47F05 General theory of partial differential operators (should also be assigned at least one other classification number in Section 47-XX)
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