Higher Monotonicity Properties of Certain Sturm-Liouville Functions. III
- 1 December 1970
- journal article
- Published by Canadian Mathematical Society in Canadian Journal of Mathematics
- Vol. 22 (6) , 1238-1265
- https://doi.org/10.4153/cjm-1970-142-1
Abstract
A Sturm-Liouville function is simply a non-trivial solution of the Sturm-Liouville differential equation (1.1) considered, together with everything else in this study, in the real domain. The associated quantities whose higher monotonicity properties are determined here are defined, for fixed λ > –1, to be (1.2) where y(x) is an arbitrary (non-trivial) solution of (1.1) and x1, x2, … is any finite or infinite sequence of consecutive zeros of any non-trivial solution z(x) of (1.1) which may or may not be linearly independent of y(x). The condition λ > –1 is required to assure convergence of the integral defining Mk, and the function W(x) is taken subject to the same restriction.Keywords
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- Aufgaben und Lehrsätze aus der AnalysisPublished by Springer Nature ,1954