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Search: MSC category 46G20 ( Infinite-dimensional holomorphy [See also 32-XX, 46E50, 46T25, 58B12, 58C10] )

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1. CMB 2000 (vol 43 pp. 138)

Boyd, C.
Exponential Laws for the Nachbin Ported Topology
We show that for $U$ and $V$ balanced open subsets of (Qno) Fr\'echet spaces $E$ and $F$ that we have the topological identity $$ \bigl( {\cal H}(U\times V), \tau_\omega \bigr) = \biggl( {\cal H} \Bigl( U; \bigl( {\cal H}(V), \tau_\omega \bigr) \Bigr), \tau_\omega \biggr). $$ Analogous results for the compact open topology have long been established. We also give an example to show that the (Qno) hypothesis on both $E$ and $F$ is necessary.

Categories:46G20, 18D15, 46M05

2. CMB 1997 (vol 40 pp. 356)

Mazet, Pierre
Principe du maximum et lemme de Schwarz, a valeurs vectorielles
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.
Categories:30C80, 32A30, 46G20, 52A07

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