# Técnicas en análisis lineal (y no lineal) y aplicaciones Linear (and non-linear) techniques and its applications

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Jiménez Rodríguez, Pablo (2016) Técnicas en análisis lineal (y no lineal) y aplicaciones. [Tesis]

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## Resumen (otros idiomas)

This thesis will be divided into two topics: the rst one will cover the rst chapter and will deal with a problem that took form little time ago (even though already in the second half of the past century there would be some results). We will be interested on nding algebraic structures (vector spaces, algebras, Banach spaces) contained in subsets of functions whose elements ful ll some anti-intuitive property, union the zero function. Thereby, we can have an idea of how the intuition may mislead us, and hint that, even though we may think that because of having to spend a huge e ort in nding one example of such elements we may not nd many more, in fact there are enough to consider huge spaces all whose elements except from the zero element satisfy the same property. More speci cally, we de ne a subset of a topological vector space to be {u100000}lineable (for a cardinal number ) if we can nd a vector space of dimension contained in the set (union the zero element, in case it is not included). If the vector space is closed, then we will be talking about {u100000}spaceability (and we will say that the set is {u100000}spaceable), and if the structure included is a Banach algebra then we will de ne the set to be ( ; ){u100000}algebrable (where here would be the cardinality of a minimal set of generators of the algebra). If no cardinal number is de ned, then we will assume the structure to be in nite dimensional. This trend was developed as an independent theory in the end of the last Century, in [5], and since its appearance it has resulted in a fruitful eld of study, as the amount of results show (see for example [4], [7], [12], [24], [26] or [54], a very recent and detailed paper giving an exhausting overview of the results published until 2014 can be found in [16]). The sets that will be considered here when studying those anti-intuitive properties will deal with functions de ned over the real line, more concretely results that lie beneath the de nition of di erentiability (for example the relationship between bounds of the di erential and the Lipschitzianity of the function). In particular, we will revisit the famous example given by Weierstrass. There will also be some sections dedicated to the analyticity of real functions and its relation with the in nite di erentiability...

Tipo de documento:Tesis

Directores (o tutores):
NombreEmail del director (o tutor)
Seoane Sepúlveda, Juan B.
Muñoz Fernández, Gustavo A.
Palabras clave:Análisis matemático
Palabras clave (otros idiomas):Mathematical analysis
Materias:Ciencias > Matemáticas > Análisis matemático
Código ID:38788