Hostname: page-component-848d4c4894-wg55d Total loading time: 0 Render date: 2024-05-15T15:18:06.326Z Has data issue: false hasContentIssue false

The Closed Ideals in an Algebra of Analytic Functions

Published online by Cambridge University Press:  20 November 2018

Walter Rudin*
Affiliation:
University of Rochester
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Let K and C be the closure and boundary, respectively, of the open unit disc U in the complex plane. Let be the Banach algebra whose elements are those continuous complex functions on K which are analytic in U, with norm

(f ∊ ).

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1957

References

1. Beurling, Anne, On two problems concerning linear transformations in Hilbert space, Acta Math., 81 (1949), 239255.Google Scholar
2. Fatou, P., Séries trigonométriques et séries de Taylor, Acta Math., 30 (1906), 335400.Google Scholar
3. Loomis, L. H., An Introduction to Abstract Harmonic Analysis (New York, 1953).Google Scholar
4. Lusin, N. and Priwaloff, J., Sur l'unicité et la multiplicité des fonctions analytiques, Ann. Sci. Ec. Norm. Sup., 42 (1925), 143191.Google Scholar
5. Nevanlinna, Rolf, Eindeutige analytische Funktionen (Berlin, 1936).Google Scholar
6. Riesz, F. and M., Ueber die Randwerte einer analytischen Funktion, Quatrième congrès des math, scand., 1916, 2744.Google Scholar
7. Saks, Stanislaw, Theory of the Integral (Warsaw, 1937).Google Scholar