A σ-operator on a complexification of an -vector space is an operator such that , where denotes the Weierstrass σ-function. In this paper, we define the notion of strongly pseudo-real σ-operator and prove that there is a one-to-one correspondence between real mixed Hodge structures and strongly pseudo-real σ-operators.
Un σ-opérateur sur la complexification dʼun espace vectoriel réel est un opérateur tel que , où est la fonction σ de Weierstrass. Dans cet article, nous introduisons la notion de σ-opérateur fortement pseudo-réel et démontrons quʼil y a une correspondance biunivoque entre les structures de Hodge mixtes réelles et les σ-opérateurs fortement pseudo-réels.
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Grzegorz Banaszak 1; Jan Milewski 2
@article{CRMATH_2013__351_13-14_551_0, author = {Grzegorz Banaszak and Jan Milewski}, title = {Mixed {Hodge} structures and {Weierstrass} \protect\emph{\ensuremath{\sigma}}-function}, journal = {Comptes Rendus. Math\'ematique}, pages = {551--555}, publisher = {Elsevier}, volume = {351}, number = {13-14}, year = {2013}, doi = {10.1016/j.crma.2013.07.015}, language = {en}, }
Grzegorz Banaszak; Jan Milewski. Mixed Hodge structures and Weierstrass σ-function. Comptes Rendus. Mathématique, Volume 351 (2013) no. 13-14, pp. 551-555. doi : 10.1016/j.crma.2013.07.015. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2013.07.015/
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