author = "Seoane-Sepúlveda, Juan B."

## Grothendieck's theorem for absolutely summing multilinear operators is optimal

Description: Grothendieck's theorem asserts that every continuous linear operator from ℓ1 to ℓ2 is absolutely (1;1)-summing. In this note we prove that the optimal constant gm so that every continuous m-linear operator from ℓ1×⋯×ℓ1 to ℓ2 is absolutely (gm;1)-summing is 2m+1. We also show that if gm<2m+1 there is...
Language(s): Inglés

## Linear chaos for the Quick-Thinking-Driver model

Description: The final publication is available at Springer via http://dx.doi.org/10.1007/s00233-015-9704-6 , In recent years, the topic of car-following has experimented an increased importance in traffic engineering and safety research. This has become a very interesting topic because of the development of drive...
Language(s): Inglés

## Algebrability of the set of non-convergent Fourier series

Description: We show that, given a set E subset of T of measure zero, the set of continuous functions whose Fourier series expansion is divergent at any point t is an element of E is dense-algebrable, i.e. there exists an infinite-dimensional, infinitely generated dense subalgebra, of C(T) every non-zero element...
Language(s): Español

## The Bohr radius of the $n$-dimensional polydisk is equivalent to $\ sqrt {\ frac {\ log n}{n}}$

Description: We show that the Bohr radius of the polydisk $\mathbb D^n$ behaves asymptotically as $\sqrt{(\log n)/n}$. Our argument is based on a new interpolative approach to the Bohnenblust--Hille inequalities which allows us to prove that the polynomial Bohnenblust--Hille inequality is subexponential.
Language(s): Inglés

## Distributional chaos for the Forward and Backward Control traffic model

Description: The interest in car-following models has increased in the last years due to its connection with vehicle-to-vehicle communications and the development of driverless cars. Some non-linear models such as the Gazes–Herman–Rothery model were already known to be chaotic. We consider the linear Forward and...
Language(s): Inglés

## On very non-linear subsets of continuous functions

Description: In this paper we continue the study initiated by Gurariy and Quarta in 2004 on the existence of linear spaces formed, up to the null vector, by continuous functions that attain the maximum only at one point. Inserting a topological flavor to the subject, we prove that results already known for funct...
Language(s): Inglés

## Hölder's inequality: some recent and unexpected applications

Description: Holder's inequality, since its appearance in 1888, has played a fundamental role in Mathematical Analysis and may be considered a milestone in Mathematics. It may seem strange that, nowadays, it keeps resurfacing and bringing new insights to the mathematical community. In this survey we show how a v...
Language(s): Inglés

## When the Identity Theorem "seems" to fail

Description: The Identity Theorem states that an analytic function (real or complex) on a connected domain is uniquely determined by its values on a sequence of distinct points that converge to a point of its domain. This result is not true in general in the real setting if we relax the analyticity hypothesis on...
Language(s): Inglés

## Smooth functions with uncountably many zeros

Description: In this short note we show that there exist uncountably generated algebras every non-zero element of which is a smooth function having uncountably many zeros. This result complements some recent ones by Enflo et al. [7, 9].
Language(s): Inglés

## Polynomial Inequalities on the π/4-Circle Sector

Description: A number of sharp inequalities are proved for the space P (2D (π/4)) of 2-homogeneous polynomials on ℝ2 endowed with the supremum norm on the sector D (π/4) := {eiθ : θ ∈ [0, π/4]}. Among the main results we can find sharp Bernstein and Markov inequalities and the calculation of the polarization con...
Language(s): Inglés