On the analyticity of WLUD∞ functions of one variable and WLUD∞ functions of several variables in a complete non-Archimedean valued field

DOI10.1017/S001309152200027XMaRDI QIDQ5043292

Khodr Shamseddine

Publication date: 21 October 2022

Published in: Proceedings of the Edinburgh Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2108.12933

zbMATH Keywords

analytic functionsTaylor series expansionnon-Archimedean analysisnon-Archimedean-valued fields

Mathematics Subject Classification ID

Functional analysis over fields other than (mathbb{R}) or (mathbb{C}) or the quaternions; non-Archimedean functional analysis (46S10) Series expansions (e.g., Taylor, Lidstone series, but not Fourier series) (41A58) Non-Archimedean valued fields (12J25) Calculus of functions taking values in infinite-dimensional spaces (26E20) Non-Archimedean analysis (32P05)

Cites Work

• Analysis on the Levi-Civita field and computational applications
• Fields: Algebraically closed and others
• Summary on non-Archimedean valued fields
• Calculus on a non-Archimedean field extension of the real numbers: inverse function theorem, intermediate value theorem and mean value theorem
• Taylor's theorem, the inverse function theorem and the implicit function theorem for weakly locally uniformly differentiable functions on non-Archimedean spaces
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