Gateaux differentiability in the Banach space of meromorphic functions
Sanjay Mallick, Debmalya Sain
TL;DR
This paper characterizes Gateaux differentiability in the Banach space of meromorphic functions using Birkhoff-James orthogonality, introducing the concept of extended orthogonality covering set to refine previous results.
Contribution
It provides a complete characterization of Gateaux differentiability for meromorphic functions and introduces the EOCS concept for refined analysis.
Findings
Complete characterization of Gateaux differentiability
Introduction of extended orthogonality covering set (EOCS)
Refinements of earlier results on analytic functions
Abstract
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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAdvanced Banach Space Theory