Let be a mapping from an open set in into , with . To say that preserves Brownian motion, up to a random change of clock, means that is harmonic and that its tangent linear mapping in proportional to a co-isometry. In the case , , such conditions signify that corresponds to an analytic function of one complex variable. We study, essentially that case , , in which we prove in particular that such a mapping cannot be “inner” if it is not trivial. A similar result for , would solve a classical conjecture on analytic functions of two complex variables.
Soit une application d’un ouvert dans , avec . Dire que conserve le mouvement brownien, à changement de temps aléatoire près, signifie que est harmonique et que son application linéaire tangente est en chaque point une co-isométrie. Dans le cas , , ces conditions indiquent que correspond à une fonction analytique d’une variable complexe. Nous étudions, essentiellement, les cas , où nous montrons en particulier qu’une telle application ne peut être “intérieure” sans être triviale. Un résultat analogue pour , permettrait de résoudre une conjecture classique sur les fonctions analytiques de deux variables.
@article{AIF_1979__29_1_207_0, author = {Bernard, Alain and Campbell, Eddy A. and Davie, A. M.}, title = {Brownian motion and generalized analytic and inner functions}, journal = {Annales de l'Institut Fourier}, pages = {207--228}, publisher = {Institut Fourier}, address = {Grenoble}, volume = {29}, number = {1}, year = {1979}, doi = {10.5802/aif.735}, mrnumber = {81b:30088}, zbl = {0386.30029}, language = {en}, url = {http://www.numdam.org/articles/10.5802/aif.735/} }
TY - JOUR AU - Bernard, Alain AU - Campbell, Eddy A. AU - Davie, A. M. TI - Brownian motion and generalized analytic and inner functions JO - Annales de l'Institut Fourier PY - 1979 SP - 207 EP - 228 VL - 29 IS - 1 PB - Institut Fourier PP - Grenoble UR - http://www.numdam.org/articles/10.5802/aif.735/ DO - 10.5802/aif.735 LA - en ID - AIF_1979__29_1_207_0 ER -
%0 Journal Article %A Bernard, Alain %A Campbell, Eddy A. %A Davie, A. M. %T Brownian motion and generalized analytic and inner functions %J Annales de l'Institut Fourier %D 1979 %P 207-228 %V 29 %N 1 %I Institut Fourier %C Grenoble %U http://www.numdam.org/articles/10.5802/aif.735/ %R 10.5802/aif.735 %G en %F AIF_1979__29_1_207_0
Bernard, Alain; Campbell, Eddy A.; Davie, A. M. Brownian motion and generalized analytic and inner functions. Annales de l'Institut Fourier, Volume 29 (1979) no. 1, pp. 207-228. doi : 10.5802/aif.735. http://www.numdam.org/articles/10.5802/aif.735/
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