Valence and oscillation of functions in the unit disk
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Date
2008
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SUOMALAINEN TIEDEAKATEMIA
Abstract
We investigate the number of times that nontrivial solutions of equations u '' + p(z)u = 0 in the unit disk can vanish-or, equivalently, the number of times that solutions of S(f) = 2p(z) can attain their values-given a restriction vertical bar p(z)vertical bar < b(vertical bar z vertical bar). We establish a bound for that number when b satisfies a Nehari-type condition, identify perturbations of the condition that, allow the number to be infinite, and compare those results with their analogs for real equations phi '' + q(t)phi = 0 in (-1, 1).
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Keywords
valence, oscillation, Schwarzian derivative