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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(Unpublished)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 |
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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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