Analytic functionals annihilated by ideals
Let V be a n-dimensional Stein manifold, I be a closed ideal of holomorphic functions on V. It was proved by Roger Gay that, given an analytic functional T such that hT = 0 (as a functional) for any h ∈ I, one can find some (n, n) compactly supported current T̃, such that T̃(φ) = 0 for any φ ∈ Iε0,0...
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| Autores principales: | , |
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1996
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| Acceso en línea: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00252611_v90_n2_p175_Dickenstein http://hdl.handle.net/20.500.12110/paper_00252611_v90_n2_p175_Dickenstein |
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| Sumario: | Let V be a n-dimensional Stein manifold, I be a closed ideal of holomorphic functions on V. It was proved by Roger Gay that, given an analytic functional T such that hT = 0 (as a functional) for any h ∈ I, one can find some (n, n) compactly supported current T̃, such that T̃(φ) = 0 for any φ ∈ Iε0,0(V) and T̃(h) = T̃(h) for any h analytic on V. In this paper, we give some explicit construction of T̃ in terms of residual currents when I is defined as a complete intersection or is locally Cohen-Macaulay. Moreover, by means of integral representation formulas of the Andersson-Berndtsson-Passare type, we also study the non complete intersection case in order to represent analytic functionals orthogonal to the ideal in terms of currents annihilated (as currents) by some power (less than n) of the local integral closure of Iε0,0(V). |
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