Generalized weyl circles
Weyl circles are studied for second order, formally selfadjoint ordinary differential equations Su=λ r(x)u on a half-open interval, first for equations with r(x) ≥ 0. It is then indicated how the study carries over to equations of polar type, provided S possesses a non-negative Dirichlet integral. Finally the method is applied to such equations but in an interesting situation recently introduced by Atkinson, Everitt and Ong. The theory is then based upon a not necessarily non-negative form. Hilbert space theories are referred to in the next, but only for motivation, and conditions for them are not deliberated. The paper is the result of stimulating discussions with W.N. Everitt during the author's visit to Dundee, September–November 1973.
KeywordsHermitean Form Symmetric Boundary Point Case Symmetric Boundary Condition Hilbert Space Theory
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