Minimal interpolation for harmonic functions

Eliyahu Beller, Stephen D. Fisher, Bernard Pinchuk

Research output: Contribution to journalArticlepeer-review

Abstract

Let K be a closed convex set in C and let z be distinct points in the open unit disc of the complex plane, with no z-n = 0. A description is given of those functionsof minimal h norm which satisfy the interpolation conditions (f(z 1), f(z n l))eK. The unique extremal is found in the case when n=1. The situation when one of the interpolation points is the origin is analyzed as well. A slightly more general problem is examined in h for 1 p oo the results here are more routine and are included for completeness.

Original languageEnglish
Pages (from-to)297-304
Number of pages8
JournalJournal of the London Mathematical Society
Volumes2-25
Issue number2
DOIs
StatePublished - Apr 1982

Bibliographical note

Funding Information:
Research of the second author was supported in part by the National Science Foundation, U.S.A. Research of the third author was supported in part by the Israel Commission for Basic Research. Research of the third author was done partly at the Forschungsinstitut fur Mathematik, E.T.H., Zurich, Switzerland, whose support is gratefully acknowledged.

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