On a generalization of the corona problem
Let g,f1,…,fm∈H∞(Δ). We provide conditions on f1,…,fm in order that |g(z)|≤|f1(z)|+…+|fm(z)|, for all z in Δ, imply that g, or g2, belong to the ideal generated by f1,…,fm in H∞.
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Wiley
1986-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171286000959 |
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| _version_ | 1832545651749027840 |
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| author | Graziano Gentili Daniele C. Struppa |
| author_facet | Graziano Gentili Daniele C. Struppa |
| author_sort | Graziano Gentili |
| collection | DOAJ |
| description | Let g,f1,…,fm∈H∞(Δ). We provide conditions on f1,…,fm in order that |g(z)|≤|f1(z)|+…+|fm(z)|, for all z in Δ, imply that g, or g2, belong to the ideal generated by f1,…,fm in H∞. |
| format | Article |
| id | doaj-art-780d5525cd934475858db582edc82d7b |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1986-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-780d5525cd934475858db582edc82d7b2025-02-03T07:25:12ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251986-01-019478578910.1155/S0161171286000959On a generalization of the corona problemGraziano Gentili0Daniele C. Struppa1Scuola Normale Superiore, Piazza dei Cavalieri, 7, Pisa 56100 , ItalyScuola Normale Superiore, Piazza dei Cavalieri, 7, Pisa 56100 , ItalyLet g,f1,…,fm∈H∞(Δ). We provide conditions on f1,…,fm in order that |g(z)|≤|f1(z)|+…+|fm(z)|, for all z in Δ, imply that g, or g2, belong to the ideal generated by f1,…,fm in H∞.http://dx.doi.org/10.1155/S0161171286000959corona problemcongenial functions. |
| spellingShingle | Graziano Gentili Daniele C. Struppa On a generalization of the corona problem International Journal of Mathematics and Mathematical Sciences corona problem congenial functions. |
| title | On a generalization of the corona problem |
| title_full | On a generalization of the corona problem |
| title_fullStr | On a generalization of the corona problem |
| title_full_unstemmed | On a generalization of the corona problem |
| title_short | On a generalization of the corona problem |
| title_sort | on a generalization of the corona problem |
| topic | corona problem congenial functions. |
| url | http://dx.doi.org/10.1155/S0161171286000959 |
| work_keys_str_mv | AT grazianogentili onageneralizationofthecoronaproblem AT danielecstruppa onageneralizationofthecoronaproblem |