We prove that a lower bound for the angle of the sector of analyticity of not necessarily symmetric submarkovian semigroups generated by second order elliptic operators in divergence form or by Ornstein–Uhlenbeck in is given by . If the semigroup is symmetric then we recover known results. In general, this lower bound is optimal.
Nous prouvons qu'une borne inférieure de l'angle du secteur d'analyticité de semi-groupes sous-markoviens non nécessairement symétriques qui sont engendrés par des opérateurs elliptiques sous forme divergencielle ou par des opérateurs de Ornstein–Uhlenbeck dans est donnée par la formule . Si le semi-groupe est symétrique on retrouve alors des résultats connus. En général, cette borne inférieure est optimale.
Accepted:
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Ralph Chill 1; Eva Fašangová 2; Giorgio Metafune 3; Diego Pallara 3
@article{CRMATH_2006__342_12_909_0,
author = {Ralph Chill and Eva Fa\v{s}angov\'a and Giorgio Metafune and Diego Pallara},
title = {The sector of analyticity of nonsymmetric submarkovian semigroups generated by elliptic operators},
journal = {Comptes Rendus. Math\'ematique},
pages = {909--914},
publisher = {Elsevier},
volume = {342},
number = {12},
year = {2006},
doi = {10.1016/j.crma.2006.04.003},
language = {en},
}
TY - JOUR AU - Ralph Chill AU - Eva Fašangová AU - Giorgio Metafune AU - Diego Pallara TI - The sector of analyticity of nonsymmetric submarkovian semigroups generated by elliptic operators JO - Comptes Rendus. Mathématique PY - 2006 SP - 909 EP - 914 VL - 342 IS - 12 PB - Elsevier DO - 10.1016/j.crma.2006.04.003 LA - en ID - CRMATH_2006__342_12_909_0 ER -
%0 Journal Article %A Ralph Chill %A Eva Fašangová %A Giorgio Metafune %A Diego Pallara %T The sector of analyticity of nonsymmetric submarkovian semigroups generated by elliptic operators %J Comptes Rendus. Mathématique %D 2006 %P 909-914 %V 342 %N 12 %I Elsevier %R 10.1016/j.crma.2006.04.003 %G en %F CRMATH_2006__342_12_909_0
Ralph Chill; Eva Fašangová; Giorgio Metafune; Diego Pallara. The sector of analyticity of nonsymmetric submarkovian semigroups generated by elliptic operators. Comptes Rendus. Mathématique, Volume 342 (2006) no. 12, pp. 909-914. doi : 10.1016/j.crma.2006.04.003. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2006.04.003/
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