Browsing by Author "Duren, Peter"
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- ItemOSCILLATION OF SOLUTIONS OF LINEAR DIFFERENTIAL EQUATIONS(CAMBRIDGE UNIV PRESS, 2009) Chuaqui, Martin; Duren, Peter; Osgood, Brad; Stowe, DennisIn this note we study the zeros of solutions of differential equations of the form u '' + pu = 0. A criterion for oscillation is found, and some sharper forms of the Sturm comparison theorem are given.
- ItemSCHWARZIAN DERIVATIVES OF CONVEX MAPPINGS(SUOMALAINEN TIEDEAKATEMIA, 2011) Chuaqui, Martin; Duren, Peter; Osgood, BradA simple proof is given for Nehari's theorem that an analytic function f which maps the unit disk onto a convex region has Schwarzian norm parallel to f parallel to <= 2. The inequality in sharper form leads to the conclusion that no convex mapping with parallel to f parallel to = 2 can map onto a quasidisk. In particular, every bounded convex mapping has Schwarzian norm parallel to f parallel to < 2. The analysis involves a structural formula for the pre-Schwarzian of a convex mapping, which is studied in further detail.