Journal ArticleDOI
Algebras in sets of queer functions
Frédéric Bayart,Lucas Quarta +1 more
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TLDR
In this article, it was shown that the set of continuous interpolating functions with big algebras contains a big algebraic structure, and that the Dirichlet series of continuous functions have a big algebraic structure as well.Abstract:
We show that the set of continuous nowhere differentiable functions, the set of Dirichlet series which are bounded in the right half-plane and diverge everywhere on the imaginary axis, and the set of continuous interpolating functions contain big algebras.read more
Citations
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Journal ArticleDOI
Linear subsets of nonlinear sets in topological vector spaces
TL;DR: The lineability and spaceability of algebraic structures has been studied extensively in real and complex analysis, operator theory, summability theory, polynomials in Banach spaces, hypercyclicity and chaos, and general functional analysis as mentioned in this paper.
Journal ArticleDOI
On dense-lineability of sets of functions on R
TL;DR: A subset M of a topological vector space X is said to be dense-lineable in X if there exists an infinite dimensional linear manifold in M ∪ { 0 } and dense in X as mentioned in this paper.
Journal ArticleDOI
Sierpinski-Zygmund functions and other problems on lineability
TL;DR: In this article, large algebraic structures inside the following sets of pathological functions were found: (i) perfectly everywhere surjective functions, (ii) differentiable functions with almost nowhere continuous derivatives, (iii) completely differentiable nowhere monotone functions, and (iv) Sierpinski-Zygmund functions.
Journal ArticleDOI
Lineability and additivity in R(R).
TL;DR: In this article, the authors give a condition for a family of functions to be lineable by means of its additivity, and use this relation to give a general method to find the lineability of large families of functions.
Journal ArticleDOI
Uncountably Generated Algebras of Everywhere Surjective Functions
TL;DR: In this paper, it was shown that there exists an algebra every non-zero element of which is an everywhere surjective function on C, that is, a function f : C -> C such that, for every non void open set U subset of C, f(U) = C.
References
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Book
An Introduction to Harmonic Analysis
TL;DR: In this article, the convergence of Fourier series on T and convergence of the conjugate function on T was studied, where T is the length of the line of a vector.
Book
Functional Analysis and Infinite-Dimensional Geometry
TL;DR: In this article, the basic concepts in Banach spaces are discussed, including weak topologies, uniform convexity, smoothness and structure, and weakly compactly generated spaces.
Journal ArticleDOI
Lineability and spaceability of sets of functions on R
TL;DR: In this article, it was shown that there is an infinite-dimensional vector space of differentiable functions on R, every non-zero element of which is nowhere monotone.
Book ChapterDOI
On O-Minimal Hybrid Systems
TL;DR: It is shown that this can be done for a quite general class of hybrid systems defined on o-minimal structures, and the problem reduces in building a finite symbolic dynamical system for the continuous dynamics of each location.
Journal ArticleDOI
On lineability of sets of continuous functions
Vladimir I. Gurariy,Lucas Quarta +1 more
TL;DR: In this paper, the existence of vector spaces of dimension at least two of continuous functions on (subsets of) R, every non-zero element of which admits one and only one absolute maximum is studied.