Abstract
We study holomorphic solutions for convolution equations in tube domains. Let be the sheaf of holomorphic functions in tube domains on the purely imaginary space and the complex $0\rightarrow \mathscr{O}^{\tau}\rightarrow \mathscr{O}^{\tau}\mu*\rightarrow 0$ generated by the convolution operator with hyperfunction kernel . In this paper, we give a new definition of "the characteristic set" Char using terms of zeros of the total symbol of , and show, under the abstract condition , 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 of coincides with the characteristics Char.
Citation
Yasunori OKADA. "On the characteristics for convolution equations in tube domains." J. Math. Soc. Japan 52 (3) 535 - 544, July, 2000. https://doi.org/10.2969/jmsj/05230535
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