Related papers: Anti M-Weierstrass function sequences
Superstring compactifications have been vigorously studied for over four decades, and have flourished involving an active iterative feedback between physics and (complex) algebraic geometry. This led to an unprecedented wealth of…
An $m$-sequence is the one of the largest period among those produced by a linear feedback shift register. It possesses several desirable features of pseudorandomness such as balance, uniform pattern distribution and ideal autocorrelation…
In this paper we give a simple proof of inequalities of integrals of functions which are the composition of nonnegative continous convex functions on a vector space ${\bf R}^m$ and vector-valued functions in a weakly compact subset of a…
We investigate structural implications arising from the condition that a given directed graph does not interpret, in the sense of primitive positive interpretation with parameters or orbits, every finite structure. Our results generalize…
Certain notions of convergence of sequences functions such as pointwise convergence and (uniform) convergence on compact or bounded sets come from suitable topological function spaces; see [1]. Under certain conditions these topologies…
In this work, we look into some results about dense subspaces of $C[0,1]$. Being our starting point the Weierstrass' Approximation Theorem, we study generalization of this in two directions: the first one studying subspaces which also have…
A correspondence between arbitrary Fourier series and certain analytic functions on the unit disk of the complex plane is established. The expression of the Fourier coefficients is derived from the structure of complex analysis. The…
The edge-of-the-wedge theorem in several complex variables gives the analytic continuation of functions defined on the poly upper half plane and the poly lower half plane, the set of points in $\mathbb{C}^d$ with all coordinates in the…
Previous results on certain sampling series have left open if divergence only occurs for certain subsequences or, in fact, in the limit. Here we prove that divergence occurs in the limit. We consider three canonical reconstruction methods…
We construct differential algebras in which spaces of (one-dimensional) periodic ultradistributions are embedded. By proving a Schwartz impossibility type result, we show that our embeddings are optimal in the sense of being consistent with…
We introduce the notions of a mutually algebraic structures and theories and prove many equivalents. A theory $T$ is mutually algebraic if and only if it is weakly minimal and trivial if and only if no model $M$ of $T$ has an expansion…
Let $X$ and $M$ be a topological space and metric space, respectively. If $C(X,M)$ denotes the set of all continuous functions from X to M, we say that a subset $Y$ of $X$ is an \emph{$M$-interpolation set} if given any function $g\in M^Y$…
We study some topological properties of maximal ideal spaces of certain algebras of almost periodic functions. Our main result is that such spaces are contractible. We present certain corollaries of this result.
We consider sequences of operators $U_n:L^1(X)\to M(X)$, where $X$ is a space of homogeneous type. Under certain conditions on the operators $U_n$ we give a complete characterization of convergence (divergence) sets of functional sequences…
We show that the set of Lebesgue integrable functions in $[0,1]$ which are nowhere essentially bounded is spaceable, improving a result from [F. J. Garc\'{i}a-Pacheco, M. Mart\'{i}n, and J. B. Seoane-Sep\'ulveda. \textit{Lineability,…
While many inner model theoretic combinatorial principles are incompatible with large cardinal axioms, on some rare occasions, large cardinals actually imply that the structure of the universe of sets is analogous to the canonical inner…
We introduce two new operations (compositional products and implication) on Weihrauch degrees, and investigate the overall algebraic structure. The validity of the various distributivity laws is studied and forms the basis for a comparison…
Metric mean dimension is a geometric invariant of dynamical systems with infinite topological entropy. We relate this concept with the fractal structure of the phase space and the H\"older regularity of the map. Afterwards we improve our…
We show that for arbitrary linearly ordered set $X$ any bounded family of (not necessarily, continuous) real valued functions on $X$ with bounded total variation does not contain independent sequences. We obtain generalized Helly's…
We consider various collections of functions from the Baire space X into itself naturally arising in (effective) descriptive set theory and general topology, including computable (equivalently, recursive) functions, contraction mappings,…