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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Extension of hyperfunction solutions of linear differential equations with constant coefficients


Author: Takahiro Kawai
Journal: Proc. Amer. Math. Soc. 59 (1976), 311-316
MSC: Primary 58G05; Secondary 35E10, 46F15, 32D15
DOI: https://doi.org/10.1090/S0002-9939-1976-0423426-5
MathSciNet review: 0423426
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Abstract: We prove the local extensibility across a $k$-convex hypersurface of solutions of a system of linear differential equations with constant coefficients which satisfies some algebraic conditions determined by $k$. A global extensibility is also proved in the case of completely $k$-convex set.


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Keywords: System of linear differential equations with constant coefficients, <IMG WIDTH="17" HEIGHT="21" ALIGN="BOTTOM" BORDER="0" SRC="images/img2.gif" ALT="$k$">-convex set, hyperfunctions, flabbiness, functor <!– MATH $\operatorname {Hom} (M,\, \cdot )$ –> <IMG WIDTH="101" HEIGHT="41" ALIGN="MIDDLE" BORDER="0" SRC="images/img1.gif" ALT="$\operatorname {Hom} (M,\, \cdot )$">
Article copyright: © Copyright 1976 American Mathematical Society