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We study spectral properties of boundary integral operators which naturally arise in the study of the Maxwell system of equations in a Lipschitz domain ฮฉ โ R 3 . By employing Rellich-type identities we show that the spectrum of the magnetic dipole boundary integral operator (composed with an appropriate projection) acting on L 2 (โฮฉ) lies in the exterior of a hyperbola whose shape depends only on the Lipschitz constant of ฮฉ. These spectral theory results are then used to construct generalized Neumann series solutions for boundary value problems associated with the Maxwell system and to study their rates of convergence.
๐ SIMILAR VOLUMES
## The Krein-von Neumann extension and its connection to an abstract buckling problem We prove the unitary equivalence of the inverse of the Krein-von Neumann extension (on the orthogonal complement of its kernel) of a densely defined, closed, strictly positive operator, S โฅ ฮตI H for some ฮต > 0 in
We solve a boundary interpolation problem at a real point for generalized Nevanlinna functions, and use the result to prove uniqueness theorems for generalized Nevanlinna functions.
## Local energy decay for a class of hyperbolic equations with constant coefficients near infinity A uniform local energy decay result is derived to a compactly perturbed hyperbolic equation with spatial variable coefficients. We shall deal with this equation in an N -dimensional exterior domain w