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Principe du maximum et lemme de Schwarz, a valeurs vectorielles

  Published:1997-09-01
 Printed: Sep 1997
  • Pierre Mazet
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Abstract

Nous {\'e}tablissons un th{\'e}or{\`e}me pour les fonctions holomorphes {\`a} valeurs dans une partie convexe ferm{\'e}e. Ce th{\'e}or{\`e}me pr{\'e}cise la position des coefficients de Taylor de telles fonctions et peut {\^e}tre consid{\'e}r{\'e} comme une g{\'e}n{\'e}ralisation des in{\'e}galit{\'e}s de Cauchy. Nous montrons alors comment ce th{\'e}or{\`e}me permet de retrouver des versions connues du principe du maximum et d'obtenir de nouveaux r{\'e}sultats sur les applications holomorphes {\`a} valeurs vectorielles.
Keywords: Principe du maximum, lemme de Schwarz, points extr{émaux. Principe du maximum, lemme de Schwarz, points extr{émaux.
MSC Classifications: 30C80, 32A30, 46G20, 52A07 show english descriptions Maximum principle; Schwarz's lemma, Lindelof principle, analogues and generalizations; subordination
Other generalizations of function theory of one complex variable (should also be assigned at least one classification number from Section 30) {For functions of several hypercomplex variables, see 30G35}
Infinite-dimensional holomorphy [See also 32-XX, 46E50, 46T25, 58B12, 58C10]
Convex sets in topological vector spaces [See also 46A55]
30C80 - Maximum principle; Schwarz's lemma, Lindelof principle, analogues and generalizations; subordination
32A30 - Other generalizations of function theory of one complex variable (should also be assigned at least one classification number from Section 30) {For functions of several hypercomplex variables, see 30G35}
46G20 - Infinite-dimensional holomorphy [See also 32-XX, 46E50, 46T25, 58B12, 58C10]
52A07 - Convex sets in topological vector spaces [See also 46A55]
 

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