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...

Descripción completa

Guardado en:
Detalles Bibliográficos
Autores principales: Dickenstein, Alicia Marcela, Sessa, Carmen I.
Publicado: 1996
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
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_00252611_v90_n2_p175_Dickenstein
record_format dspace
spelling paper:paper_00252611_v90_n2_p175_Dickenstein2023-06-08T14:52:49Z Analytic functionals annihilated by ideals Dickenstein, Alicia Marcela Sessa, Carmen I. 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). Fil:Dickenstein, A. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Sessa, C. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 1996 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
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
description 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).
author Dickenstein, Alicia Marcela
Sessa, Carmen I.
spellingShingle Dickenstein, Alicia Marcela
Sessa, Carmen I.
Analytic functionals annihilated by ideals
author_facet Dickenstein, Alicia Marcela
Sessa, Carmen I.
author_sort Dickenstein, Alicia Marcela
title Analytic functionals annihilated by ideals
title_short Analytic functionals annihilated by ideals
title_full Analytic functionals annihilated by ideals
title_fullStr Analytic functionals annihilated by ideals
title_full_unstemmed Analytic functionals annihilated by ideals
title_sort analytic functionals annihilated by ideals
publishDate 1996
url 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
work_keys_str_mv AT dickensteinaliciamarcela analyticfunctionalsannihilatedbyideals
AT sessacarmeni analyticfunctionalsannihilatedbyideals
_version_ 1768543883224940544

Ejemplares similares