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manuscripta mathematica

, Volume 1, Issue 3, pp 231–240 | Cite as

Ordnungseigenschaften holomorpher Funktionen

  • Georg Aumann
Article
  • 16 Downloads

Abstract

A linear geometric order theory for holomorphic mappings F: ℂn→ℂm is given if a family of linear subspaces L of ℂn×ℂm is specified; the theory then is concerned with the order number of connected parts of the intersections L∩ (F) of the L's with the graph (F) of F. For m=1 (i.e. case of one function) it is proved that the local linear order number of a holomorphic function is finite in every point. If the L's are real-linear subspaces then real differential geometric methods lead to the proof, if the L's are complex-linear then ideal-theoretical means do.

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Literatur

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    G. AUMANN, Über lokale Ordnungseigenschaften der konformen Abbildungen, J. reine und angewandte Mathematik 178, 187–191 (1938);Google Scholar
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    O. HAUPT - H. KÜNNETH, Geometrische Ordnungen, Berlin 1967;Google Scholar
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    R.C. GUNNING - H. ROSSI, Analytic Functions of Several Complex Variables, Prentice-Hall Series 1965;Google Scholar
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    H. SONNER, Über Ordnungseigenschaften von analytischen Abbildungen zweier komplexer Veränderlicher (Dissertation Universität München 1954);Google Scholar
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    K. ZARISKI - P. SAMUEL, Commutative Algebra, Princeton, N.J., 1958.Google Scholar

Copyright information

© Springer-Verlag 1969

Authors and Affiliations

  • Georg Aumann
    • 1
  1. 1.Mathematisches Institut der TH München8 München

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