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 language | English |
|---|---|
| Pages (from-to) | 297-304 |
| Number of pages | 8 |
| Journal | Journal of the London Mathematical Society |
| Volume | s2-25 |
| Issue number | 2 |
| DOIs | |
| State | Published - 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.
Funding
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.
| Funders | Funder number |
|---|---|
| Israel Commission for Basic Research | |
| National Science Foundation |