Open Access
July, 2000 On the characteristics for convolution equations in tube domains
Yasunori OKADA
J. Math. Soc. Japan 52(3): 535-544 (July, 2000). DOI: 10.2969/jmsj/05230535


We study holomorphic solutions for convolution equations in tube domains. Let Oτ be the sheaf of holomorphic functions in tube domains on the purely imaginary space -1Rn and S the complex $0\rightarrow \mathscr{O}^{\tau}\rightarrow \mathscr{O}^{\tau}\mu*\rightarrow 0$ generated by the convolution operator μ* with hyperfunction kernel μ. In this paper, we give a new definition of "the characteristic set" Char(μ*) using terms of zeros of the total symbol of μ*, and show, under the abstract condition (S), the equivalence between two notions of characteristics outside of the zero section $T^{*}_{\sqrt{-1}^R^{n}}(\sqrt{-1}R^{n})$. Moreover we conclude that the micro-support SS(S) of S coincides with the characteristics Char(μ*).


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Yasunori OKADA. "On the characteristics for convolution equations in tube domains." J. Math. Soc. Japan 52 (3) 535 - 544, July, 2000.


Published: July, 2000
First available in Project Euclid: 10 June 2008

zbMATH: 0967.45002
MathSciNet: MR1760603
Digital Object Identifier: 10.2969/jmsj/05230535

Primary: 44A35
Secondary: 46F15

Keywords: characteristics , convolution equations , micro-supports

Rights: Copyright © 2000 Mathematical Society of Japan

Vol.52 • No. 3 • July, 2000
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