Vol. 49, No. 2, 1973

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Analytic structure in the spectrum of a natural system

Robert Morgan Brooks

Vol. 49 (1973), No. 2, 315–334

Let [X,A] be a natural syslem such that X is locally compact and every open subset of X is σ-compact. Let 𝒜 be the sheaf on X generated by the presheaf {U AU A|U}. If p X,V is a subvariety of an open sei in Cn which contains 0 and if there exists an algebra homomorphism φ : 𝒜p V 𝒪0 having rank greater than one, lken there exists a neighborhood U of p in X, a neighborhood of 0 in Cn and a continuous map τ;V ω U sueh that (1) τ(0) = p, (2) if f AU, lhen f t is holomorphic on V ω (3) if f AU, then (f τ)0 = φ((f)p), where (f τ)0 is the germ at 0 of f τ and (f)p is the elemeRl of 𝒜p (the stalk of 𝒜 above p) determined by f.

Mathematical Subject Classification 2000
Primary: 46J10
Secondary: 32E25
Received: 30 August 1972
Published: 1 December 1973
Robert Morgan Brooks