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Analytic functionals annihilated by ideals

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Abstract

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\(\tilde T\), such that\(\tilde T(\varphi ) = 0\) for any ϕ ∈Iɛ 0,0(V) and T(h)=\(\tilde T(h)\) for any h analytic on V. In this paper, we give some explicit construction of Ť 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 ofIɛ0,0.

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Authors and Affiliations

  1. Departamento de Matemática, F.C.E. y N, Universidad de Buenos Aires, Ciudad Universitaria-Pab. I (1428), Buenos Aires, Argentina

    Alicia Dickenstein & Carmen Sessa

  2. Département de Mathématiques, Université Bordeaux I, 33405, Talence-Cedex, France

    Roger Gay & Alain Yger

Authors
  1. Alicia Dickenstein
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  2. Roger Gay
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  3. Carmen Sessa
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  4. Alain Yger
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Dickenstein, A., Gay, R., Sessa, C. et al. Analytic functionals annihilated by ideals. Manuscripta Math 90, 175–223 (1996). https://doi.org/10.1007/BF02568302

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