Characteristic Cauchy problems in the complex domain

Yasunori Okada () and Hideshi Yamane ()
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Yasunori Okada: Chiba University, Department of Mathematics and Informatics, Faculty of Science
Hideshi Yamane: Chiba Institute of Technology, Mathematics

A chapter in New Trends in Microlocal Analysis, 1997, pp 69-80 from Springer

Abstract: 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 (search for similar items in EconPapers)
Date: 1997
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DOI: 10.1007/978-4-431-68413-8_5

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