Hostname: page-component-cd9895bd7-dk4vv Total loading time: 0 Render date: 2024-12-24T01:12:55.077Z Has data issue: false hasContentIssue false
  • English
  • Français

Norm preserving interpolation sets for polydisc algebras

Published online by Cambridge University Press:  24 October 2008

Josep Globevnik
Josep Globevnik
Affiliation:
E.K. University of Ljubljana, Yugoslavia
Get access Rights & Permissions [Opens in a new window]

Abstract

Let N > 1 and let AN be the polydisc algebra, i.e. the algebra of all continuous functions on the closed polydisc δ¯N ⊂ N, analytic on the open polydisc δN, with sup norm. Call a closed set F ⊂ δ¯N a peak interpolation set for AN if given any f ε C(F), f ≠ 0, there is an extension f ε AN of f such that ¦f˜(z)¦ < ‖ f ‖ (z ε δ¯N - F); call F a norm preserving interpolation set for AN if given any f ε C(F) there is an extension f˜ ε AN of f such that ‖f˜‖ = ‖f‖. The paper gives a complete description of norm preserving interpolation sets for AN in terms of peak interpolation sets for AM, M ≤ N.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 91 , Issue 2 , March 1982 , pp. 291 - 303
Copyright
Copyright © Cambridge Philosophical Society 1982

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Rudin, W.Function theory in polydiscs (Benjamin, New York, Amsterdam 1969), see also the Russian translation containing additional bibliography (Mir, Moscow, 1974).Google Scholar
(2)Rudin, W. and Stout, E. L.Boundary properties of functions of several complex variables. J. Math. Mech. 14 (1965), 991–1006.Google Scholar
(3)Stout, E. L.The theory of uniform algebras (Bogden and Quigley, Tarrytown-on-Hudson, N.Y. 1971).Google Scholar