On étudie ici quelques espaces de fonctions holomorphes dans des domaines localement convexes, ayant comme cas particuliers les espaces de Fock holomorphes. Les espaces duaux sont caractérisés avec la transformation de Fourier-Borel pour des types d’holomorphie appropriés. On montre que ces espaces de fonctions sont de Fréchet-Schwartz (resp. de Silva, resp. nucléaires) quand leurs domaines sont des espaces de Silva (resp. de Fréchet-Schwartz, resp. nucléaires). Les conditions de croissance
Dual pairs of spaces of holomorphic functions on locally convex domains are studied, yielding the holomorphic Fock spaces as particular cases. The duality is with respect to the Fourier-Borel transformation for appropriate holomorphy types. These functions spaces are shown to be Fréchet-Schwartz spaces (resp. Silva spaces, resp. nuclear). The
@article{AIF_1976__26_4_151_0, author = {Dwyer III, Thomas A. W.}, title = {Dualit\'e des espaces de fonctions enti\`eres en dimension infinie}, journal = {Annales de l'Institut Fourier}, pages = {151--195}, publisher = {Imprimerie Durand}, address = {Chartres}, volume = {26}, number = {4}, year = {1976}, doi = {10.5802/aif.636}, mrnumber = {58 #2276}, zbl = {0331.46039}, language = {fr}, url = {http://www.numdam.org/articles/10.5802/aif.636/} }
TY - JOUR AU - Dwyer III, Thomas A. W. TI - Dualité des espaces de fonctions entières en dimension infinie JO - Annales de l'Institut Fourier PY - 1976 SP - 151 EP - 195 VL - 26 IS - 4 PB - Imprimerie Durand PP - Chartres UR - http://www.numdam.org/articles/10.5802/aif.636/ DO - 10.5802/aif.636 LA - fr ID - AIF_1976__26_4_151_0 ER -
%0 Journal Article %A Dwyer III, Thomas A. W. %T Dualité des espaces de fonctions entières en dimension infinie %J Annales de l'Institut Fourier %D 1976 %P 151-195 %V 26 %N 4 %I Imprimerie Durand %C Chartres %U http://www.numdam.org/articles/10.5802/aif.636/ %R 10.5802/aif.636 %G fr %F AIF_1976__26_4_151_0
Dwyer III, Thomas A. W. Dualité des espaces de fonctions entières en dimension infinie. Annales de l'Institut Fourier, Tome 26 (1976) no. 4, pp. 151-195. doi : 10.5802/aif.636. http://www.numdam.org/articles/10.5802/aif.636/
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