On functions subharmonic in a half-space
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- by Alfred Huber
- Trans. Amer. Math. Soc. 82 (1956), 147-159
- DOI: https://doi.org/10.1090/S0002-9947-1956-0078464-3
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References
- Lars V. Ahlfors, On Phragmén-Lindelöf’s principle, Trans. Amer. Math. Soc. 41 (1937), no. 1, 1–8. MR 1501888, DOI 10.1090/S0002-9947-1937-1501888-X
- Ralph Philip Boas Jr., Entire functions, Academic Press, Inc., New York, 1954. MR 0068627 M. Brelot, Étude des fonctions sousharmoniques au voisinage d’un point, Actualités Scientifiques et Industrielles, no. 139, Paris, Hermann, 1934.
- Marcel Brelot, Étude des fonctions sous-harmoniques au voisinage d’un point singulier, Ann. Inst. Fourier (Grenoble) 1 (1949), 121–156 (1950) (French). MR 37416 A. Dinghas, Ueber das Phragmén-Lindelöfsche Prinzip und den Julia-Carathéodoryschen Satz, Preuss. Akad. Wiss. Sitzungsber. (1938) pp. 32-48.
- Alexander Dinghas, Über positive harmonische Funktionen in einem Halbraum, Math. Z. 46 (1940), 559–570 (German). MR 3334, DOI 10.1007/BF01181454
- J. L. Doob and B. O. Koopman, On analytic functions with positive imaginary parts, Bull. Amer. Math. Soc. 40 (1934), no. 8, 601–605. MR 1562915, DOI 10.1090/S0002-9904-1934-05926-3
- Maurice Heins, On the Phragmén-Lindelöf principle, Trans. Amer. Math. Soc. 60 (1946), 238–244. MR 19117, DOI 10.1090/S0002-9947-1946-0019117-0
- Jacqueline Lelong-Ferrand, Sur le principe de Julia-Carathéodory et son extension à l’espace à $p$-dimensions, Bull. Sci. Math. (2) 73 (1949), 5–16 (French). MR 31602
- L. H. Loomis and D. V. Widder, The Poisson integral representation of functions which are positive and harmonic in a half-plane, Duke Math. J. 9 (1942), 643–645. MR 7200
- Albert Pfluger, À propos d’un mémoire récent de M. Brelot, Ann. Inst. Fourier (Grenoble) 2 (1950), 81–82 (1951) (French). MR 44676 F. Riesz, Sur les fonctions subharmoniques et leur rapport à la théorie du potentiel, parts I and II, Acta Math. vol. 48 (1926) pp. 329-343 and vol. 54 (1930) pp. 321-360. M. Riesz, Sur certaines inégalités dans la théorie des fonctions avec quelques remarques sur les géométries non-euclidiennes, Kungl. Fysiogr. Sällsk. Lund För. vol. 1 (1938). M. Tsuji, On a positive harmonic function in a half-plane, Jap. J. Math. vol. 15 (1938) pp. 277-285. S. Verblunsky, On positive harmonic functions in a half-plane, Proc. Cambridge Philos. Soc. vol. 31 (1935) pp. 482-507.
- Alexander Weinstein, Discontinuous integrals and generalized potential theory, Trans. Amer. Math. Soc. 63 (1948), 342–354. MR 25023, DOI 10.1090/S0002-9947-1948-0025023-X
- Alexander Weinstein, Generalized axially symmetric potential theory, Bull. Amer. Math. Soc. 59 (1953), 20–38. MR 53289, DOI 10.1090/S0002-9904-1953-09651-3 E. T. Whittaker and G. N. Watson, A course of modern analysis, 4th ed., Cambridge, 1927.
Bibliographic Information
- © Copyright 1956 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 82 (1956), 147-159
- MSC: Primary 31.0X
- DOI: https://doi.org/10.1090/S0002-9947-1956-0078464-3
- MathSciNet review: 0078464