George A. Hufford

Abstract: When wave propagation through a stratified atmosphere is formulated in operator theoretic terms, it becomes evident that the problem does not follow the guide of the usual examples of mathematical physics. Nevertheless, such a formulation is useful to reveal why many of the usual procedures are valid and where they may be deficient. In particular, even if the refractivity profile is merely required to belong to a general class of perhaps badly discontinuous functions, the problem always has a well–behaved solution that may be subjected to a modal analysis. On the other hand, the resulting mode series converges neither rapidly nor uniformly, and, as the asymptotic behavior of the modes shows, one is advised to use that series only with caution.

Keywords: radio wave propagation; Airy functions; contraction semi-groups; creeping wave modes; modal analysis; stratified atmospheres; wave guide modes; weak convergence

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