Hostname: page-component-848d4c4894-2pzkn Total loading time: 0 Render date: 2024-06-03T12:35:42.124Z Has data issue: false hasContentIssue false
  • English
  • Français

Exceptional sets with respect to order of integral functions of two variables

Published online by Cambridge University Press:  24 October 2008

Ronald Maude
Ronald Maude
Affiliation:
University College of WalesAberystwyth
Get access Rights & Permissions [Opens in a new window]

Extract

1. Introduction. The definition of the order of an integral function of one complex variable extends immediately to integral functions of several complex variables to give us their total order. In the case of integral functions of two complex variables, Lelong(5) has shown that the order on any analytic plane through the origin is equal to the total order except for an exceptional set of planes of exterior capacity 0 on which the order is less than the total order.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 53 , Issue 2 , April 1957 , pp. 323 - 342
Copyright
Copyright © Cambridge Philosophical Society 1957

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Bochner, S. and Martin, W. T.Several complex variables (Princeton, 1948).Google Scholar
(2)Cartan, H.Sur les systèmes de fonctions holomorphes à variétés linéaires lacunaires et leurs applications. Ann. sci. Éc. norm. sup., Paris, (3) 45 (1928), 265–346.Google Scholar
(3)Hausdorff, F.Dimension und aussers Mass. Math. Ann. 79 (1919), 157–9.CrossRefGoogle Scholar
(4)Kneser, H.Zur Theorie der gebrochenen mehrerer Veranderlicher. Jber. Dtsch. MatVer. (1) (1938), 1–22.Google Scholar
(5)Lelong, P.Sur quelques problèmes de la théorie des fonctions de deux variables complexes. Ann. sci. Éc. norm. sup., Paris, (3) 58 (1941), 83–177.CrossRefGoogle Scholar
(6)Nevanlinna, R.Eindeutige analytische Functionen, 2te. Aufle. (Springer-Verlag, 1953).CrossRefGoogle Scholar
(7)Titchmarsh, E. C.The theory of functions, 2nd ed. (Oxford, 1939).Google Scholar