Hostname: page-component-848d4c4894-sjtt6 Total loading time: 0 Render date: 2024-07-06T11:55:28.107Z Has data issue: false hasContentIssue false

On Some Families of Analytic Functions on Riemann Surfaces

Published online by Cambridge University Press:  22 January 2016

Shinji Yamashita*
Affiliation:
Mathematical Institute, Nagoya University
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Throughout this paper all functions are single-valued. Let R be a Riemann surface. We shall denote by φ the least harmonic majorant of a function φ defined in R if it has the meaning.

Type
Research Article
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1968

References

[1] Brelot, M.: Sur la théorie autonome des fonctions sousharmoniques; Bull. Sc. Math., 65 (1941), 7298.Google Scholar
[2] Brelot, M.: Éléments de la théorie classique du potentiel; Les Cours de Sorbonne, C.D.U., Paris, (1959), 3rd edition (1965).Google Scholar
[3] Constantinescu, C. and Cornea, A.: Ideale Ränder Riemannscher Flächen; Springer, Berlin, (1963).CrossRefGoogle Scholar
[4] Doob, J.L.: Probability method applied to the first boundary value problem; Proc. 3rd Berkeley Symp. Math. Statis. Prob., 2 (1956), 4980.Google Scholar
[5] Doob, J.L.: A non-probabilistic proof of the relative Fatou theorem; Ann. Inst. Fourier, 9 (1959), 293300.CrossRefGoogle Scholar
[6] Doob, J.L.: Boundary properties of functions with finite Dirichlet integrals; Ann. Inst. Fourier, 12 (1962), 573621.Google Scholar
[7] Gårding, L. and Hörmander, L.: Strongly subharmonic functions; Math. Scand., 15 (1964), 9396.CrossRefGoogle Scholar
[8] Gehring, F.W.: The asymptotic values for analytic functions with bounded characteristic; Quart. J. Math. Oxford, 9 (1958), 2829.Google Scholar
[9] Heins, M.: Lindelöfian maps; Ann. Math., 62 (1955), 418446.CrossRefGoogle Scholar
[10] Myrberg, P.J.: Über die analytische Fortsetzung von beschränkten Funktionen; Ann. Acad. Sci. Fenn. A.I, 58 (1949).Google Scholar
[11] Naïn, L.: Sur le rôle de la frontière de R.S. Martin dans la théorie du potentiel; Ann. Inst. Fourier, 7 (1957), 183281.Google Scholar
[12] Nevanlinna, R.: Eindeutige analytische Funktionen; Springer, Berlin, (1953).Google Scholar
[13] Parreau, M.: Sur les moyennes des fonctions harmoniques et analytiques et la classification des surfaces de Riemann; Ann. Inst. Fourier, 3 (1952), 103197.Google Scholar
[14] Riesz, F. and Riesz, M.: Über die Randwerte einer analytischen Funktion; C.R. Congr. Math. Scand. Stockholm, (1916), 2744.Google Scholar
[15] Rudin, W.: Analytic functions of class Hp ; Trans. Amer. Math. Soc., 78 (1955), 4666.Google Scholar
[16] Smirnov, V.I.: Sur les formules de Cauchy et de Green et quelques problèmes qui s’y rattachent; Izv. AN SSSR, ser. fiz.-mat., 3 (1932), 337372.Google Scholar
[17] Tumarkin, G. Ts. and Havinson, S. Ya.: On removal of singularities of analytic functions of a class (class D); Uspehi Matem. Nauk, 12 (1957), 1939. (Russian).Google Scholar
[18] la Vallée Poussin, C. de: Sur l’integrale de Lebesgue; Trans. Amer. Math. Soc., 16 (1915), 435501.Google Scholar