Hostname: page-component-848d4c4894-5nwft Total loading time: 0 Render date: 2024-06-09T14:02:17.985Z Has data issue: false hasContentIssue false
  • English
  • Français

On Pseudo-Analytic Functions

Published online by Cambridge University Press:  22 January 2016

D. A. Storvick
D. A. Storvick*
Affiliation:
Department of Mathematics, University of Minnesota, Minneapolis, Minnesota
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.

Many of the properties of analytic functions can be proved in a purely topological manner, so that such properties are then valid for the larger class of functions which are topologically equivalent to analytic functions. The importance of such functions has been recognized fairly recently, particularly in the theory of partial differential equations, where certain solutions have been shown to possess the topological properties of analytic functions, i.e., interiority and continuity, but not necessarily the analytic properties of complex differentiability and integrability.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 12 , December 1957 , pp. 131 - 138
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1957

References

[ 1 ] Bagemihl, F., Curvilinear cluster sets of arbitrary functions, Proc. Nat. Acad. Sci. (U.S.A.), 41, no. 6 (1955), pp. 379–382.CrossRefGoogle ScholarPubMed
[ 2 ] Jenkins, J. A., On Quasiconformal mappings, Journal of Rational Mechanics and Analysis, 5 (1956), pp. 343–352.Google Scholar
[ 3 ] Lohwater, A. J., The boundary values of a class of meromorphic functions, Duke Math. Journal, 19 (1952), pp. 243–252.CrossRefGoogle Scholar
[ 4 ] Lohwater, A. J., Les valeurs asymptotiques de quelques fonctions méromorphes dans le cercle-unité, C. R. Acad. Sci. Paris, 237 (1953), pp. 16–18.Google Scholar
[ 5 ] Lohwater, A. J., The reflection principle and the distribution of values of functions defined in a circle, Ann. Acad. Sci. Fennicae A. I., 229 (1956), pp. 1–18.Google Scholar
[ 6 ] Nevanlinna, R., Eindeutige analytische Funktionen, 2nd ed. Berlin (1953).Google Scholar
[ 7 ] Noshiro, K., A theorem on the cluster sets of pseudo analytic functions, Nagoya Math. Journal, I (1950), pp. 83–89.CrossRefGoogle Scholar
[ 8 ] Noshiro, K., On the theory of cluster sets of analytic functions, Sugaku, 5, no. 2 (1953), pp. 65–72 (Japanese).Google Scholar
[ 9 ] Pfluger, A., Extremalldngen und Kapazität, Comment. Math. Helv., 29 (1955), 120–131.CrossRefGoogle Scholar
[10] Seidel, W., On the distribution of values of bounded analytic functions, Trans. Amer. Math. Soc, 36 (1934), 201–226.CrossRefGoogle Scholar
[11] Stoïlow, S., Leçons sur les principes topologiques de la théorie des fonctions analytiques, Paris (1938).Google Scholar
[12] Storvick, D. A., On meromorphic functions of bounded characteristic, Proc. Amer. Math. Soc, 8 (1957), 32–38.CrossRefGoogle Scholar
[13] Whyburn, G. T., Analytic Topology, Amer. Math. Soc. Colloq. Pub., 28 (1942).Google Scholar