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Minimal Interpolation for Harmonic Functions
Author(s) -
Beller Eliyahu,
Fisher Stephen D.,
Pinchuk Bernard
Publication year - 1982
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/s2-25.2.297
Subject(s) - interpolation (computer graphics) , mathematics , norm (philosophy) , regular polygon , combinatorics , harmonic , mathematical analysis , pure mathematics , geometry , computer science , physics , artificial intelligence , motion (physics) , quantum mechanics , political science , law
Let K be a closed convex set in C n and let z 1 ,…, z n be distinct points in the open unit disc of the complex plane, with no z j = 0. A description is given of those functions f of minimal h 1 norm which satisfy the interpolation conditions ( f(z 1 ),…, f(z n ))ε K . 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 p for 1 < p ⩽ ∞ the results here are more routine and are included for completeness.