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...
Guardado en:
| Autores principales: | , , , |
|---|---|
| Formato: | JOUR |
| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_00252611_v90_n2_p175_Dickenstein |
| Aporte de: |
| id |
todo:paper_00252611_v90_n2_p175_Dickenstein |
|---|---|
| record_format |
dspace |
| spelling |
todo:paper_00252611_v90_n2_p175_Dickenstein2023-10-03T14:35:39Z Analytic functionals annihilated by ideals Dickenstein, A. Gay, G. Sessa, C. Yger, A. 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. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar 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). |
| format |
JOUR |
| author |
Dickenstein, A. Gay, G. Sessa, C. Yger, A. |
| spellingShingle |
Dickenstein, A. Gay, G. Sessa, C. Yger, A. Analytic functionals annihilated by ideals |
| author_facet |
Dickenstein, A. Gay, G. Sessa, C. Yger, A. |
| author_sort |
Dickenstein, A. |
| 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 |
| url |
http://hdl.handle.net/20.500.12110/paper_00252611_v90_n2_p175_Dickenstein |
| work_keys_str_mv |
AT dickensteina analyticfunctionalsannihilatedbyideals AT gayg analyticfunctionalsannihilatedbyideals AT sessac analyticfunctionalsannihilatedbyideals AT ygera analyticfunctionalsannihilatedbyideals |
| _version_ |
1807324114721964032 |