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- W2023016813 abstract "Thus far we have studied in [1], [2] and [4] the possibility of extension of solutions of linear partial differential equations p(D)u = Q with constant coefficients to various exceptional sets. There, the exceptional sets were of those types to which the convex analysis, or the technique of the Fourier transform based on the growth order estimation, was applicable. Here we treat a new kind of exceptional set. Let K = {(0,..., 0, x,,); — 1 <*„<!} be the line segment on the x,raxis of the n-dimensional Euclidean space R. Let U be an open neighborhood of K. (This means that U contains K as a closed subset.) Let &p and jtfp be the hyperfunction and the real analytic solutions of p(D)u = 0 respectively. We give a necessary and sufficient condition on p(D) for 0p(UK)l&jy) = Q, where 0^) = (l/)/0p[K], and a sufficient condition for jtfp(UK)l<stfp(U) = Q. (See Theorem 1.4 and Corollary 2.4.) Let L be the closure of K. In the course of proof we must reduce the support of a hyperfunction from L to LK under some additional condition. Since the convex hull of LK agrees with L, the routine technique in the Fourier transform based on the growth condition has no use. Instead, we rely on a new tool for non-convex Fourier analysis developed in [6]. (See Lemma 2.2 below.)" @default.
- W2023016813 created "2016-06-24" @default.
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- W2023016813 date "1975-01-01" @default.
- W2023016813 modified "2023-09-25" @default.
- W2023016813 title "On linear exceptional sets of solutions of linear partial differential equations with constant coefficients" @default.
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- W2023016813 doi "https://doi.org/10.2977/prims/1195191471" @default.
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