Topological properties of the Fréchet space of holomorphic functions of several complex variables
Let p( n) ( > 1) be the Privalov class of holomorphic functions on the unit ball n in the space of -complex variables. The class p( n) ( > 1), equipped with the topology given by a natural metric, becomes an -algebra. In this paper, we shall introduce a Fréchet space Fp( n) ( > 1) of holomo...
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| Published in: | Mathematica Montisnigri Vol. 58; pp. 5 - 16 |
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| Main Author: | |
| Format: | Journal Article |
| Language: | English Japanese |
| Published: |
Keldysh Institute of Applied Mathematics
01.01.2023
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| ISSN: | 0354-2238, 2704-4963 |
| Online Access: | Get full text |
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| Summary: | Let p( n) ( > 1) be the Privalov class of holomorphic functions on the unit ball n in the space of -complex variables. The class p( n) ( > 1), equipped with the topology given by a natural metric, becomes an -algebra. In this paper, we shall introduce a Fréchet space Fp( n) ( > 1) of holomorphic functions on n which contains p( n). Moreover, we shall characterize some topological properties of Fp( n) induced by the family of semi norms on Fp( n) . |
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| ISSN: | 0354-2238 2704-4963 |
| DOI: | 10.20948/mathmontis-2023-58-1 |