Spectral study of holomorphic functions with bounded growth

Ivan Cnop

Annales de l'institut Fourier (1972)

  • Volume: 22, Issue: 2, page 293-309
  • ISSN: 0373-0956

Abstract

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This paper studies properties of a large class of algebras of holomorphic functions with bounded growth in several complex variables.The main result is useful in the applications. Using the symbolic calculus of L. Waelbroeck, it gives for instance a theorem of the “Nullstellensatz” type and approximation theorems.

How to cite

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Cnop, Ivan. "Spectral study of holomorphic functions with bounded growth." Annales de l'institut Fourier 22.2 (1972): 293-309. <http://eudml.org/doc/74080>.

@article{Cnop1972,
abstract = {This paper studies properties of a large class of algebras of holomorphic functions with bounded growth in several complex variables.The main result is useful in the applications. Using the symbolic calculus of L. Waelbroeck, it gives for instance a theorem of the “Nullstellensatz” type and approximation theorems.},
author = {Cnop, Ivan},
journal = {Annales de l'institut Fourier},
language = {eng},
number = {2},
pages = {293-309},
publisher = {Association des Annales de l'Institut Fourier},
title = {Spectral study of holomorphic functions with bounded growth},
url = {http://eudml.org/doc/74080},
volume = {22},
year = {1972},
}

TY - JOUR
AU - Cnop, Ivan
TI - Spectral study of holomorphic functions with bounded growth
JO - Annales de l'institut Fourier
PY - 1972
PB - Association des Annales de l'Institut Fourier
VL - 22
IS - 2
SP - 293
EP - 309
AB - This paper studies properties of a large class of algebras of holomorphic functions with bounded growth in several complex variables.The main result is useful in the applications. Using the symbolic calculus of L. Waelbroeck, it gives for instance a theorem of the “Nullstellensatz” type and approximation theorems.
LA - eng
UR - http://eudml.org/doc/74080
ER -

References

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  1. [1] H. BUCHWALTER, Topologies, bornologies et compactologies. Thesis, Fac. des Sciences, Univ. de Lyon, 1968. Zbl0205.41601
  2. [2] I. CNOP, Un problème de spectre dans certaines algèbres de fonctions holomorphes à croissance tempérée, C.R. Acad. Sci., Paris, A 270, 1970, 1690-1691. Zbl0194.44502MR42 #3574
  3. [3] I. CNOP, A theorem concerning holomorphic functions with bounded growth, Thesis, Univ. of Brussels, 1971. 
  4. [4] I. CNOP, Un űNullstellensatzƇ pour les fonctions holomorphes à croissance, Colloque International d'Analyse Fonctionnelle, Bordeaux (to appear). Zbl0249.46012
  5. [5] I. CNOP and J.-P. FERRIER, Existence de fonctions spectrales et densité pour les algèbres de fonctions holomorphes avec croissance. C.R. Acad. Sci., Paris, A 273, 1971, 353-355. Zbl0223.46033MR45 #4152
  6. [6] J.-P. FERRIER, Séminaire sur les algèbres complètes, Lecture Notes in Mathematics, 164, Springer, 1970. Zbl0203.13203MR42 #5050
  7. [7] J.-P. FERRIER, Approximation des fonctions holomorphes de plusieurs variables avec croissance, C.R. Acad. Sci., Paris, A 271, 1970, 722-724. Zbl0198.46003MR42 #8262
  8. [8] J.-P. FERRIER, Approximation avec croissance des fonctions holomorphes de plusieurs variables, Ann. Inst. Fourier, Grenoble, XXII, 1 (1972). Zbl0219.32009MR49 #633
  9. [9] J.-P. FERRIER, Sur la convexité holomorphe et les limites inductives d'algèbres O(δ). C.R. Acad. Sci., Paris, A 272, 1971, 237-239. Zbl0214.14001MR43 #5297
  10. [10] J.-P. FERRIER, Application à l'analyse complexe du calcul symbolique de L. Waelbroeck, Cours Peccot au Collège de France, 1971. 
  11. [11] L. HÖRMANDER, L2 Estimates and existence theorems for the ∂ operator, Acta Math., 113, 1965, 89-152. Zbl0158.11002
  12. [12] L. HÖRMANDER, Generators for some rings of analytic functions. Bull. Amer. Math. Soc., 73, 1967, 943-949. Zbl0172.41701MR37 #1977
  13. [13] J. J. KELLEHER and B. A. TAYLOR, Finitely generated ideals in rings of analytic functions, Math. Ann., 193, 1971, 225-237. Zbl0207.12906MR46 #2077
  14. [14] L. WAELBROECK, Étude spectrale des algèbres complètes. Acad. Roy. Belgique, Mém. Cl. des Sci., 1960. Zbl0193.10005MR22 #8355
  15. [15] L. WAELBROECK, Lectures in spectral theory, Dep. of Math., Yale Univ., 1963. 
  16. [16] L. WAELBROECK, About a spectral theorem, Function algebras (edit. by F. Birtel), Scott, Foresman and Co, 1965, 310-321. Zbl0145.16801MR33 #3122
  17. [17] L. WAELBROECK, Some theorems about bounded structures, J. of Funct. Anal., 1, 4, 1967, 392-408. Zbl0201.16601MR36 #3107
  18. [18] L. WAELBROECK, Un űNullstellensatzƇ pour les fonctions holomorphes à croissance, (1970) (mimeographed). 

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