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Characteristic Cauchy problems in the complex domain

In: New Trends in Microlocal Analysis

Author

Listed:
  • Yasunori Okada

    (Chiba University, Department of Mathematics and Informatics, Faculty of Science)

  • Hideshi Yamane

    (Chiba Institute of Technology, Mathematics)

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.

Suggested Citation

  • Yasunori Okada & Hideshi Yamane, 1997. "Characteristic Cauchy problems in the complex domain," Springer Books, in: Jean-Michel Bony & Mitsuo Morimoto (ed.), New Trends in Microlocal Analysis, pages 69-80, Springer.
    • Handle: RePEc:spr:sprchp:978-4-431-68413-8_5
    DOI: 10.1007/978-4-431-68413-8_5
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