Extension of hyperfunction solutions of linear differential equations with constant coefficients

Kawai, Takahiro

doi:10.1090/S0002-9939-1976-0423426-5

Extension of hyperfunction solutions of linear differential equations with constant coefficients
HTML articles powered by AMS MathViewer

by Takahiro Kawai PDF

Proc. Amer. Math. Soc. 59 (1976), 311-316 Request permission

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.

References

Leon Ehrenpreis, Fourier analysis in several complex variables, Pure and Applied Mathematics, Vol. XVII, Wiley-Interscience [A division of John Wiley & Sons, Inc.], New York-London-Sydney, 1970. MR 0285849
Takahiro Kawai, Vanishing of cohomology groups on completely $k$-convex sets, Publ. Res. Inst. Math. Sci. 11 (1975/76), no. 3, 775–784. MR 0405512, DOI 10.2977/prims/1195191146
Takahiro Kawai, Removable singularities of solutions of systems of linear differential equations, Bull. Amer. Math. Soc. 81 (1975), 461–463. MR 372437, DOI 10.1090/S0002-9904-1975-13785-2
Hikosaburo Komatsu, Resolutions by hyperfunctions of sheaves of solutions of differential equations with constant coefficients, Math. Ann. 176 (1968), 77–86. MR 226181, DOI 10.1007/BF02052957
Hikosaburo Komatsu, Relative cohomology of sheaves of solutions of differential equations, Hyperfunctions and pseudo-differential equations (Proc. Conf., Katata, 1971; dedicated to the memory of André Martineau), Lecture Notes in Math., Vol. 287, Springer, Berlin, 1973, pp. 192–261. MR 0393874

Systèmes différentielles à coefficients constants

V. P. Palamodov, Lineĭnye differentsial′nye operatory s postoyaannymi koèffitsientami, Izdat. “Nauka”, Moscow, 1967 (Russian). MR 0243193
Mikio Sato, Theory of hyperfunctions. II, J. Fac. Sci. Univ. Tokyo Sect. I 8 (1960), 387–437 (1960). MR 132392