Soit une variété riemannienne de volume fini, l’opérateur laplacien sur . Pour certains sous-espaces des algèbres de Wiener et Royden sur , on construit une décomposition canonique liée à l’opérateur itéré . Si est une solution de l’équation biharmonique , les valeurs de et à la frontière idéale déterminent les composantes de suivant la décomposition.
Let be a smooth Riemannian manifold of finite volume, its Laplace (-Beltrami) operator. Canonical direct-sum decompositions of certain subspaces of the Wiener and Royden algebras of are found, and for biharmonic functions (those for which ) the decompositions are related to the values of the functions and their Laplacians on appropriate ideal boundaries.
@article{AIF_1971__21_3_217_0, author = {Kwon, Y. K. and Sario, Leo and Walsh, Bertram}, title = {Behavior of biharmonic functions on {Wiener's} and {Royden's} compactifications}, journal = {Annales de l'Institut Fourier}, pages = {217--226}, publisher = {Institut Fourier}, address = {Grenoble}, volume = {21}, number = {3}, year = {1971}, doi = {10.5802/aif.387}, zbl = {0208.13703}, mrnumber = {49 #5385}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.387/} }
TY - JOUR AU - Kwon, Y. K. AU - Sario, Leo AU - Walsh, Bertram TI - Behavior of biharmonic functions on Wiener's and Royden's compactifications JO - Annales de l'Institut Fourier PY - 1971 SP - 217 EP - 226 VL - 21 IS - 3 PB - Institut Fourier PP - Grenoble UR - https://aif.centre-mersenne.org/articles/10.5802/aif.387/ DO - 10.5802/aif.387 LA - en ID - AIF_1971__21_3_217_0 ER -
%0 Journal Article %A Kwon, Y. K. %A Sario, Leo %A Walsh, Bertram %T Behavior of biharmonic functions on Wiener's and Royden's compactifications %J Annales de l'Institut Fourier %D 1971 %P 217-226 %V 21 %N 3 %I Institut Fourier %C Grenoble %U https://aif.centre-mersenne.org/articles/10.5802/aif.387/ %R 10.5802/aif.387 %G en %F AIF_1971__21_3_217_0
Kwon, Y. K.; Sario, Leo; Walsh, Bertram. Behavior of biharmonic functions on Wiener's and Royden's compactifications. Annales de l'Institut Fourier, Tome 21 (1971) no. 3, pp. 217-226. doi : 10.5802/aif.387. https://aif.centre-mersenne.org/articles/10.5802/aif.387/
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