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Characteristic Cauchy problems in the complex domain

  • Yasunori Okada
  • Hideshi Yamane

Abstract

Gårding-Kotake-Leray showed that in a certain characteristic Cauchy problem
$$Pu = \upsilon \in o\;(the\;sheaf\;of\;holomorphic\;functions)$$
with zero Cauchy data on a hypersurface S, u can be ramified. Moreover, u is of the form
$$(*)\;\upsilon (x) = \sum\limits_{i = 0}^{q - 1} {\upsilon i(x){{[k(x)]}^{1/q}}} $$
where q is a positive integer ≥ 2 and u is ramified around K : k(x) = 0. Here K is tangent to S at characteristic points of S. Let us denote by \(N_{q,K}^m\) the class of functions which have the form (*) and whose first m traces on S vanish.

Keywords

Differential Operator Characteristic Point Complex Domain Cauchy Data Essential Singularity 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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    Y. Okada, H. Yamane, A characteristic Cauchy problem in the complex domain, J. Math, pures et appl, (to appear).Google Scholar

Copyright information

© Springer-Verlag Tokyo 1997

Authors and Affiliations

  • Yasunori Okada
    • 1
  • Hideshi Yamane
    • 2
  1. 1.Department of Mathematics and Informatics, Faculty of ScienceChiba UniversityYayoi-cho, Inage-ku, Chiba 263Japan
  2. 2.MathematicsChiba Institute of TechnologyShibazono, Narashino, Chiba 275Japan

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