Characteristic Cauchy problems in the complex domain

  • Yasunori Okada
  • Hideshi Yamane


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.


Differential Operator Characteristic Point Complex Domain Cauchy Data Essential Singularity 


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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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