Some properties of differentiable p-adic functions

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Fernández Sánchez, J. and Maghsoudi, S. and Rodríguez-Vidanes, D.L. and Seoane-Sepúlveda, Juan B. Some properties of differentiable p-adic functions. (Unpublished)

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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.


Item Type:Article
Uncontrolled Keywords:Algebrability; Bounded-p-adic derivativep-adic function; lineability; Lipschitz function; Strict differentiability
Palabras clave (otros idiomas):Espacios vectoriales
Subjects:Sciences > Mathematics
Sciences > Mathematics > Mathematical analysis
ID Code:73497
Deposited On:07 Jul 2022 10:42
Last Modified:07 Jul 2022 12:33

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