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Analytic Structures for H∞ of Certain Domains in Cn

Published online by Cambridge University Press:  20 November 2018

Eric P. Kronstadt
Eric P. Kronstadt*
Affiliation:
University of Michigan, Ann Arbor, Michigan
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Let Ω C Cn be a bounded domain; let H∞ (Ω) be the uniform algebra of bounded analytic functions on 12; and let ∑ (Ω) be the maximal ideal space of H∞ (Ω). In the weak-* topology of (H∞ (Ω))*, ∑ (Ω) is a compact Hausdorf space in which Ω is embedded in a natural fashion, so that to every g ∈ H∞ (Ω) there corresponds the Gelfand transform ĝ ∈ C(∑ (Ω)); ĝ|Ω = g.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 30 , Issue 4 , 01 August 1978 , pp. 863 - 871
Copyright
Copyright © Canadian Mathematical Society 1978

References

1. Bernard, A., Algebres quotients d'algèbres uniformes, Comptes Rendu Acad. Sci. Paris 272 (1971), A1101-A1104.Google Scholar
2. Carleson, L., An interpolation problem for bounded analytic functions, Amer. J. Math. 80 (1958), 921–930.Google Scholar
3. Cartan, E., Sur les domaines bornés homogènes de Vespace de n variables complexes, Abh. Math. Sem. Univ. Hamburg 7 (1935), 116–162.Google Scholar
4. Cutrer, W., On analytic structure in the maximal ideal space of H^ (Dn), Illinois J. Math. 16 (1972), 423–433.Google Scholar
5. Edwards, C. H., Jr., Advanced calculus of several variables (Academic Press, New York, 1973).Google Scholar
6. Henkin, G. M., Approximation of functions in pseudoconvex domains and the theorem of Z. Leibenzon (Russian), Bull. Acad. Polon. Sci. Ser. Sci. Math. Astron. Phys. 19 (1971), 37–42.Google Scholar
7. Hoffman, K., Bounded analytic functions and Gleason parts, Annals of Math. 86 (1967) 74–111.Google Scholar
8. Hua, L. K., Harmonic analysis of functions of several complex variables in the classical domains American Math. Soc, Providence, R.I., (1963).Google Scholar
9. Kobayashi, S., Hyperbolic manifolds and holomorphic mappings (Marcel Dekker, Inc., New York, 1970).Google Scholar
10. Kronstadt, E., Interpolating sequences in polydisks, Trans. Amer. Math. Soc. 199 (1974), 369–398.Google Scholar
11. Kronstadt, E. and Neville, C., Interpolating sequences for Hardy and Bergman classes in polydisks, to appear, Mich. Math. J.Google Scholar
12. Range, R. M., Bounded holomorphic functions on strictly pseudo-convex domains, U.C.L.A. Doctoral Dissertation, 1971.Google Scholar
13. Rosay, J. P., Une équivalence au Corona Problem dans O et un problème d'idéal dans HX(D), J. Functional Analysis 7 (1971), 71–84.Google Scholar