Asymptotics of the m-Coefficient for Eigenvalue Problems with Eigenparameter in the Boundary Conditions |
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Authors: | Fulton C. T. |
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Affiliation: | Department of Mathematics, The Pennsylvania State University University Park, PA. 16802, U.S.A. |
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Abstract: | For Sturm-Liouville problems on [a, ) with a regular -dependentboundary condition at a, and the limit point case at , a techniqueof W. N. Everitt [1] is employed to obtain asymptotic formulaefor the associated m()-functions on rays and lines in the complex-plane. The method relies on asymptotic formulae for solutionsof the initial value problem for u'+qu = u, as || ,which the author has given in [4]. For the case of the regularleft endpoint, the asymptotic formulae on vertical lines sufficeto provide a direct proof of the formula for the total variationof the associated spectral function, a question which the authorhad raised in [3; Remark 5.2]. |
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