Related papers: Achievement sets and sum ranges with ideal support…

In this article we discuss the transcendence of certain infinite sums and products by using the Subspace theorem. In particular we improve the result of Han\v{c}l and Rucki \cite{hancl3}.

In this article, we propose a general theory of integration of the Riemann and Lebesgue types with respect to arbitrary measures and functions, connected by a continuous bilinear product, with values in abstract vector spaces endowed with a…

In this paper we have extended the notion of statistical limit point as introduced by Fridy[8] to I-statistical limit point of sequences of real numbers and studied some basic properties of the set of all I-statistical limit points and…

Approximable algebras were defined by Chen in his proof of the Fujita theorem in the arithmetic context. These were shown to not be necessarily subalgebras of section rings of big line bundles in a previous prepreint of the author. Here, we…

The complex exponentials with integer frequencies form a basis for the space of square integrable functions on the unit interval. We analyze whether the basis property is maintained if the support of the complex exponentials is restricted…

Using probability theory we derive an expression for the sum of a series of definite integrals involving upper incomplete Gamma functions. In the proof, a normal variance mixture distribution with Beta mixing distributions plays a crucial…

We give $L^1$-norm estimates for exponential sums of a finite sets $A$ consisting of integers or lattice points. Under the assumption that $A$ possesses sufficient multidimensional structure, our estimates are stronger than those of…

We present a common ground for infinite sums, unordered sums, Riemann/Lebesgue integrals, arc length and some generalized means. It is based on extending functions on finite sets using Hausdorff metric in a natural way.

In this paper, we construct the abstract ideal of polynomials. We show this is an ideal of Banach and, in a second moment, we explore the question of the coherence and compatibility of the pair composed by the abstract ideals of polynomials…

There are three types of results in this paper. The first, extending a representation theorem on a conformal mapping that omits two values of equal modulus. This was due to Brickman and Wilken. They constructed a representation as a convex…

Motivated by Emmanuel Kowalski's exponential sums over definable sets in finite fields, we generalize Ax's theorem on pseudo-finite fields to a continuous-logic setting allowing for an additive character. The role played by Weil's Riemann…

This paper has a twofold purpose: to present an overview of the theory of absolutely summing operators and its different generalizations for the multilinear setting, and to sketch the beginning of a research project related to an objective…

We define and study a numerical-range analogue of the notion of spectral set. Among the results obtained are a positivity criterion and a dilation theorem, analogous to those already known for spectral sets. An important difference from the…

In this note we prove an abstract version of a result from 2002 due to Delgado and Pi\~{n}ero on absolutely summing operators. Several applications are presented; some of them in the multilinear framework and some in a completely nonlinear…

The statistical convergence is defined for sequences with the asymptotic density on the natural numbers, in general. In this paper, we introduce the statistical convergence for nets in Riesz spaces by using the finite additive measures on…

Let $\mathbb N$ be the set of positive integers, and denote by $\lambda(A)=\inf\{t>0:\sum_{a\in A} a^{-t}<\infty\}$ the convergence exponent of $A\subset\mathbb N$. For $0<q\le 1$, $0\le q\le 1$, respectively, the admissible ideals…

We consider the Ideal Proof System (IPS) introduced by Grochow and Pitassi and pose the question of which tautologies admit symmetric proofs, and of what complexity. The symmetry requirement in proofs is inspired by recent work establishing…

We solve the last standing open problem from the seminal paper by J. Gerlits and Zs. Nagy, which was later reposed by A. Miller, T. Orenshtein and B. Tsaban. Namely, we show that under p = c there is a \delta-set that is not a \gamma-set.…

Let S=K[x_1,...,x_n] be a polynomial ring. Denote by $p_a$ the power sum symmetric polynomial x_1^a+...+x_n^a. We consider the following two questions: Describe the subsets $A \subset \mathbb{N}$ such that the set of polynomials $p_a$ with…

We investigate here sums of triangular numbers $f(x):=\sum_i b_i T_{x_i}$ where $T_n$ is the $n$-th triangular number. We show that for a set of positive integers $S$ there is a finite subset $S_0$ such that $f$ represents $S$ if and only…