Implicit operator differential equations and applications to electrodynamics
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A cylindrical waveguide with layered dispersive medium is considered. An implicit operator differential equation of second order is obtained by separating variables in the corresponding boundary-value problem for Maxwell's equations. Existence and uniqueness theorems are proved and explicit formulae for solutions are given. The spectral theory of operators and operator sheaves are used.
[1] J. Goldstein. Semigroups of Linear Operators and Applications , 1985 .