On the spectrum of A(Ω) and H∞(Ω)
Urban Cegrell
Annales Polonici Mathematici, Tome 58 (1993), p. 193-199 / Harvested from The Polish Digital Mathematics Library
Access to full text
Full (PDF)

We study some properties of the maximal ideal space of the bounded holomorphic functions in several variables. Two examples of bounded balanced domains are introduced, both having non-trivial maximal ideals.

Publié le : 1993-01-01
EUDML-ID : urn:eudml:doc:262439 
@article{bwmeta1.element.bwnjournal-article-apmv58z2p193bwm,
     author = {Urban Cegrell},
     title = {On the spectrum of A($\Omega$) and $H^$\infty$($\Omega$)$
            },
     journal = {Annales Polonici Mathematici},
     volume = {58},
     year = {1993},
     pages = {193-199},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-apmv58z2p193bwm}
}

Urban Cegrell. On the spectrum of A(Ω) and $H^∞(Ω)$
            . Annales Polonici Mathematici, Tome 58 (1993) pp. 193-199. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-apmv58z2p193bwm/

[000] [1] U. Cegrell, Representing measures in the spectrum of H∞(Ω), in: Complex Analysis, Proc. Internat. Workshop, Wuppertal 1990, K. Diederich (ed.), Aspects of Math. E17, Vieweg, 1991, 77-80.

[001] [2] J. E. Fornæss and N. Øvrelid, Finitely generated ideals in A(Ω), Ann. Inst. Fourier (Grenoble) 33 (2) (1983), 77-85. | Zbl 0489.32013

[002] [3] T. W. Gamelin, Uniform Algebras, Prentice-Hall, Englewood Cliffs, N.J., 1969. | Zbl 0213.40401

[003] [4] T. W. Gamelin, Uniform Algebras and Jensen Measures, Cambridge Univ. Press, 1978.

[004] [5] M. Hakim et N. Sibony, Spectre de A(Ω̅ ) pour les domaines bornés faiblement pseudoconvexes réguliers, J. Funct. Anal. 37 (1980), 127-135. | Zbl 0441.46044

[005] [6] J. J. Kohn, Global regularity for ∂̅ on weakly pseudo-convex manifolds, Trans. Amer. Math. Soc. 181 (1973), 273-292. | Zbl 0276.35071

[006] [7] A. Noell, The Gleason problem for domains of finite type, Complex Variables 4 (1985), 233-241. | Zbl 0535.32009

[007] [8] M. Range, Holomorphic Functions and Integral Representations in Several Complex Variables, Springer, 1986. | Zbl 0591.32002

[008] [9] N. Sibony, Prolongement analytique des fonctions holomorphes bornées, in: Sém. Pierre Lelong 1972-73, Lecture Notes in Math. 410, Springer, 1974, 44-66.

[009] [10] J. Siciak, Balanced domains of holomorphy of type H∞, Mat. Vesnik 37 (1985), 134-144. | Zbl 0575.32009

[010] [11] N. Øvrelid, Generators of the maximal ideals of A(D̅), Pacific J. Math. 39 (1971), 219-223. | Zbl 0231.46090