### Abstract

An extension of a classical theorem of Rellich to the exterior of a closed proper convex cone is proved: Let Γ be a closed convex proper cone in R^{ n} and -Γ′ be the antipodes of the dual cone of Γ. Let {Mathematical expression} be a partial differential operator with constant coefficients in R^{ n}, where Q(ζ)≠0 on R^{ n}-iΓ′ and P_{ i} is an irreducible polynomial with real coefficients. Assume that the closure of each connected component of the set {ζ∈R^{ n}-iΓ′;P_{ j}(ζ)=0, grad P_{ j}(ζ)≠0} contains some real point on which grad P_{ j}≠0 and grad P_{ j}∉Γ∪(-Γ). Let C be an open cone in R^{ n}-Γ containing both normal directions at some such point, and intersecting each normal plane of every manifold contained in {ξ∈R^{ n};P(ξ)=0}. If u∈ℒ′∩L_{ loc}^{ 2} (R^{ n}-Γ) and the support of P(-i∂/∂x)u is contained in Γ, then the condition {Mathematical expression} implies that the support of u is contained in Γ.

Original language | English |
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Pages (from-to) | 193-203 |

Number of pages | 11 |

Journal | Israel Journal of Mathematics |

Volume | 31 |

Issue number | 2 |

DOIs | |

Publication status | Published - 1978 Jun 1 |

Externally published | Yes |

### ASJC Scopus subject areas

- Mathematics(all)