Interpolating sequences on convex curves in the open unit disc
Author: Dennis H. Wortman
Journal: Proc. Amer. Math. Soc. 48 (1975), 157-164
MSC: Primary 30A80; Secondary 46J15
MathSciNet review: 0361092
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Abstract: Let be the open unit disc in the complex plane, and let be the unit circle. Given a convex curve in , internally tangent to at one point, then a sequence on , successive points of which are equally spaced in the hyperbolic (Poincaré) metric, is shown to be interpolating. This result is then applied to the study of the Banach algebra . The Gleason part of a point in the maximal ideal space of which lies in the closure of a convex curve in is proved to be nontrivial. In addition, for each point in the maximal ideal space of which lies in the closure of a compact subset of union a point of , an interpolating Blaschke product is constructed whose extension to the maximal ideal space has modulus less than 1 on , and the relevance of this to the Shilov boundary of is discussed.
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Keywords: Interpolating sequence, convex curve, pseudohyperbolic metric, , maximal ideal space, Gleason part, Shilov boundary
Article copyright: © Copyright 1975 American Mathematical Society