Some properties of differentiable p-adic functions

In this paper, using the tools from the lineability theory, we distinguish certain subsets of p -adic differentiable functions. Specifically, we show that the following sets of functions are large enough to contain an infinite dimensional algebraic structure: (i) continuously differentiable but not...

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Bibliographic Details
Published in:Revista matemática complutense 2024-05, Vol.37 (2), p.391-411
Main Authors: Fernández-Sánchez, J., Maghsoudi, S., Rodríguez-Vidanes, D. L., Seoane–Sepúlveda, J. B.
Format: Article
Language:English
Subjects:
Algebra
Analysis
Applications of Mathematics
Continuity (mathematics)
Geometry
Mathematics
Mathematics and Statistics
Topology
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Summary:In this paper, using the tools from the lineability theory, we distinguish certain subsets of p -adic differentiable functions. Specifically, we show that the following sets of functions are large enough to contain an infinite dimensional algebraic structure: (i) continuously differentiable but not strictly differentiable functions, (ii) strictly differentiable functions of order r but not strictly differentiable of order r + 1 , (iii) strictly differentiable functions with zero derivative that are not Lipschitzian of any order α > 1 , (iv) differentiable functions with unbounded derivative, and (v) continuous functions that are differentiable on a full set with respect to the Haar measure but not differentiable on its complement having cardinality the continuum.
ISSN:1139-1138
1988-2807
DOI:10.1007/s13163-023-00458-1