Geodesic
On the Growth of Entire Functions Bounded on Large Sets
Canadian journal of mathematics, Tome 29 (1977) no. 6, pp. 1287-1291

Voir la notice de l'article provenant de la source Cambridge University Press

There have been many indications of a relationship between the rate of growth of an entire function and the “size” of the set, E(c), where the modulus of the function is larger than the constant, c. Theorems of this type include the classical theorem of Wiman on functions of bounded minimum modulus, the Phragmén-Lindelöf Theorem, the Denjoy-Carleman-Ahlfors Theorem, and its many subsequent improvements. These theorems can all be understood as quantitative versions of the statement that if ƒ is an entire function such that, for some c > 0, the set E(c) is ‘'small”, then the maximum modulus function M(R, f) is forced to grow rapidly with R. 
Hansen, Lowell J. On the Growth of Entire Functions Bounded on Large Sets. Canadian journal of mathematics, Tome 29 (1977) no. 6, pp. 1287-1291. doi: 10.4153/CJM-1977-128-4
@article{10_4153_CJM_1977_128_4,
     author = {Hansen, Lowell J.},
     title = {On the {Growth} of {Entire} {Functions} {Bounded} on {Large} {Sets}},
     journal = {Canadian journal of mathematics},
     pages = {1287--1291},
     year = {1977},
     volume = {29},
     number = {6},
     doi = {10.4153/CJM-1977-128-4},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1977-128-4/}
}
TY  - JOUR
AU  - Hansen, Lowell J.
TI  - On the Growth of Entire Functions Bounded on Large Sets
JO  - Canadian journal of mathematics
PY  - 1977
SP  - 1287
EP  - 1291
VL  - 29
IS  - 6
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1977-128-4/
DO  - 10.4153/CJM-1977-128-4
ID  - 10_4153_CJM_1977_128_4
ER  - 
%0 Journal Article
%A Hansen, Lowell J.
%T On the Growth of Entire Functions Bounded on Large Sets
%J Canadian journal of mathematics
%D 1977
%P 1287-1291
%V 29
%N 6
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1977-128-4/
%R 10.4153/CJM-1977-128-4
%F 10_4153_CJM_1977_128_4

[1] 1. Ahlfors, L. V., Untersuchungen zur Théorie der konformen Abbildung una der ganzen Funktionen, Acta Soc. Sci. Fenn. (2) A, 9 (1930), 1–40. Google Scholar

[2] 2. Al-Katifi, W., On the asymptotic values and paths of certain integral and meromorphie junctions, Proc. London Math. Soc. (3) 16 (1966), 599–634. Google Scholar

[3] 3. Hansen, L. J., Hardy classes and ranges of functions, Michigan Math. J. 17 (1970), 235–248. Google Scholar

[4] 4. Hansen, L. J. On the growth of entire functions which are large on small sets, Notices of Amer. Math. Soc, June 1976, (Abstract). Google Scholar

[5] 5. Hansen, L. J. and Hayman, W. K., On the growth of functions omitting large sets, Journal d'Analyse Math. 30 (1976), 208–214. Google Scholar

[6] 6. Hayman, W. K., Research problems in function theory, Proceedings of the Symposium on Complex Analysis, Canterbury 1973 (edited by J. Clunie and W. K. Hayman), London Math. Soc. Lecture Notes Series #12 (Cambridge Univ. Press, 1974), 143–180. Google Scholar

[7] 7. Kennedy, P. B., A class of integral functions bounded on certain curves, Proc. London Math. Soc. (3) 6 (1956), 518–547. Google Scholar

[8] 8. Titchmarsh, E. C., Theory of functions (2nd Edition, Oxford, 1939). Google Scholar

[9] 9. Tsuji, M., A theorem on the majoration of harmonic measure and its applications, Tôhoku Math. J. (2) 8(1951), 13–23. Google Scholar

Cité par Sources :