RT Journal Article
T1 Injective mappings in R-R and lineability
A1 Jiménez Rodríguez, P.
A1 Maghsoudi, S.
A1 Muñoz-Fernández, Gustavo A.
A1 Seoane-Sepúlveda, Juan B.
AB It is known that there is not a two dimensional linear space in R-R every non-zero element of which is an injective function. Here, we generalize this result to arbitrarily large dimensions. We also study the convolution of non differentiable functions which gives, as a result, a differentiable function. In this latter case, we are able to show the existence of linear spaces of the largest possible dimension formed by functions enjoying the previous property. By doing this we provide both positive and negative results to the recent field of lineability. Some open questions are also provided.
PB Belgian Mathematical Soc Triomphe
SN 1370-1444
YR 2016
FD 2016
LK https://hdl.handle.net/20.500.14352/23158
UL https://hdl.handle.net/20.500.14352/23158
NO Ministerio de Ciencia e Innovación (MICINN)
DS Docta Complutense
RD 8 abr 2025