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Higher Monotonicity Properties of Certain Sturm-Liouville Functions. IV

Published online by Cambridge University Press:  20 November 2018

Lee Lorch ,
Martin E. Muldoon  and
Peter Szego
Lee Lorch
Affiliation:
York University, Downsview, Ontario
Martin E. Muldoon
Affiliation:
York University, Downsview, Ontario
Peter Szego
Affiliation:
Ampex Corporation, Redwood City, California
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The Sturm-Liouville functions considered in this instalment are real (as are all other quantities discussed here) non-trivial solutions of the differential equation

1.1

Higher monotonicity properties, as defined in § 2, are investigated for a number of sequences (finite or infinite) associated with these functions. One such sequence, discussed in detail later, has the kth term

1.2

where the constant X > — 1 (to assure convergence of each integral), W(x) possesses higher monotonicity properties and, moreover, is such that, again, each integral converges, and X1, X2, … is a sequence (finite or infinite) of consecutive zeros of a solution of (1.1), which may or may not be linearly independent of y(x), in the interval of definition of the functions under consideration.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 24 , Issue 2 , April 1972 , pp. 349 - 368
Copyright
Copyright © Canadian Mathematical Society 1972

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