1. Some properties of differentiable p-adic functions.
- Author
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Fernández-Sánchez, J., Maghsoudi, S., Rodríguez-Vidanes, D. L., and Seoane–Sepúlveda, J. B.
- Abstract
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. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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