Gateaux differentiability in the Banach space of meromorphic functions
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866929569442824192 |
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| author | Mallick, Sanjay Sain, Debmalya |
| author_facet | Mallick, Sanjay Sain, Debmalya |
| contents | We study the Gateaux differentiability in the Banach space of meromorphic functions and obtain a complete characterization of the same, by using Birkhoff-James orthogonality techniques. We introduce the concept of extended orthogonality covering set (EOCS), which allows us to present refinements of some earlier results on the Gateaux differentiability of analytic functions. We also discuss some related properties of meromorphic functions which follow directly from the said characterization. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_23411 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Gateaux differentiability in the Banach space of meromorphic functions Mallick, Sanjay Sain, Debmalya Complex Variables Functional Analysis 46B20, 30D30 We study the Gateaux differentiability in the Banach space of meromorphic functions and obtain a complete characterization of the same, by using Birkhoff-James orthogonality techniques. We introduce the concept of extended orthogonality covering set (EOCS), which allows us to present refinements of some earlier results on the Gateaux differentiability of analytic functions. We also discuss some related properties of meromorphic functions which follow directly from the said characterization. |
| title | Gateaux differentiability in the Banach space of meromorphic functions |
| topic | Complex Variables Functional Analysis 46B20, 30D30 |
| url | https://arxiv.org/abs/2410.23411 |