We give a new proof of a Phragmén Lindelöf theorem due to W.H.J. Fuchs and valid for an arbitrary open subset of the complex plane: if is analytic on , bounded near the boundary of , and the growth of is at most polynomial then either is bounded or for some positive and has a simple pole.
On donne une nouvelle démonstration d’un théorème de W.H.J. Fuchs du type Phragmén Lindelöf pour les ouverts quelconques du plan ouvert : soit holomorphe dans et bornée aux environs de la frontière de croissante ou plus comme un polynôme; alors ou est bornée ou a un pôle simple à l’infini.
@article{AIF_1984__34_2_63_0, author = {Lyons, Terry J.}, title = {An application of fine potential theory to prove a {Phragmen} {Lindel\"of} theorem}, journal = {Annales de l'Institut Fourier}, pages = {63--66}, publisher = {Institut Fourier}, address = {Grenoble}, volume = {34}, number = {2}, year = {1984}, doi = {10.5802/aif.964}, mrnumber = {86c:30042}, zbl = {0522.30024}, language = {en}, url = {http://archive.numdam.org/articles/10.5802/aif.964/} }
TY - JOUR AU - Lyons, Terry J. TI - An application of fine potential theory to prove a Phragmen Lindelöf theorem JO - Annales de l'Institut Fourier PY - 1984 SP - 63 EP - 66 VL - 34 IS - 2 PB - Institut Fourier PP - Grenoble UR - http://archive.numdam.org/articles/10.5802/aif.964/ DO - 10.5802/aif.964 LA - en ID - AIF_1984__34_2_63_0 ER -
%0 Journal Article %A Lyons, Terry J. %T An application of fine potential theory to prove a Phragmen Lindelöf theorem %J Annales de l'Institut Fourier %D 1984 %P 63-66 %V 34 %N 2 %I Institut Fourier %C Grenoble %U http://archive.numdam.org/articles/10.5802/aif.964/ %R 10.5802/aif.964 %G en %F AIF_1984__34_2_63_0
Lyons, Terry J. An application of fine potential theory to prove a Phragmen Lindelöf theorem. Annales de l'Institut Fourier, Volume 34 (1984) no. 2, pp. 63-66. doi : 10.5802/aif.964. http://archive.numdam.org/articles/10.5802/aif.964/
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