We show that discrete exponentials form a basis of discrete holomorphic functions on a finite critical map. On a combinatorially convex set, the discrete polynomials form a basis as well.
Nous montrons que les exponentielles forment une base des fonctions holomorphes discrètes sur une carte critique compacte. Sur un convexe, les polynômes discrets forment également une base.
Keywords: discrete holomorphic functions, discrete analytic functions, monodriffic functions, exponentials
Mot clés : fonctions holomorphes discrètes, fonctions analytiques discrètes, exponentielles
@article{BSMF_2004__132_2_305_0, author = {Mercat, Christian}, title = {Exponentials {Form} a {Basis} of {Discrete} {Holomorphic} {Functions} on a {Compact}}, journal = {Bulletin de la Soci\'et\'e Math\'ematique de France}, pages = {305--326}, publisher = {Soci\'et\'e math\'ematique de France}, volume = {132}, number = {2}, year = {2004}, doi = {10.24033/bsmf.2467}, mrnumber = {2076370}, zbl = {1080.30042}, language = {en}, url = {http://archive.numdam.org/articles/10.24033/bsmf.2467/} }
TY - JOUR AU - Mercat, Christian TI - Exponentials Form a Basis of Discrete Holomorphic Functions on a Compact JO - Bulletin de la Société Mathématique de France PY - 2004 SP - 305 EP - 326 VL - 132 IS - 2 PB - Société mathématique de France UR - http://archive.numdam.org/articles/10.24033/bsmf.2467/ DO - 10.24033/bsmf.2467 LA - en ID - BSMF_2004__132_2_305_0 ER -
%0 Journal Article %A Mercat, Christian %T Exponentials Form a Basis of Discrete Holomorphic Functions on a Compact %J Bulletin de la Société Mathématique de France %D 2004 %P 305-326 %V 132 %N 2 %I Société mathématique de France %U http://archive.numdam.org/articles/10.24033/bsmf.2467/ %R 10.24033/bsmf.2467 %G en %F BSMF_2004__132_2_305_0
Mercat, Christian. Exponentials Form a Basis of Discrete Holomorphic Functions on a Compact. Bulletin de la Société Mathématique de France, Volume 132 (2004) no. 2, pp. 305-326. doi : 10.24033/bsmf.2467. http://archive.numdam.org/articles/10.24033/bsmf.2467/
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