Related papers: Introduction to generalised Cesaro convergence III

These notes are devoted to the theory of exponential sums over finite fields. The first chapter recalls some of the number-theoretic interest of such sums. The second chapter discusses the $L$-functions attached to such sums, the "Weil…

Data fusion techniques integrate information from heterogeneous data sources to improve learning, generalization, and decision making across data sciences. In causal inference, these methods leverage rich observational data to improve…

Quantiles, expectiles and extremiles can be seen as concepts defined via an optimization problem, where this optimization problem is driven by two important ingredients: the loss function as well as a distributional weight function. This…

The convergence of Ces\`{a}ro means of negative order of double trigonometric Fourier series of functions of bounded partial $\Lambda$-variation is investigated. The sufficient and neccessary conditions on the sequence $\Lambda…

We present Korovkin approximation theorems that incorporate summability methods. These result allows us to obtain a unified treatment of several previous results, focusing on the underlying structure and the properties that a summability…

Direct links between generalized harmonic numbers, linear Euler sums and Tornheim double series are established in a more perspicuous manner than is found in existing literature. We show that every linear Euler sum can be decomposed into a…

The conditions for convergence of square and rectangular Fejer means of functions on the infinite dimensional torus were obtained, also a generalization of the results for the case of abstract measure spaces was formulated.

With thousands of academic articles shared on a daily basis, it has become increasingly difficult to keep up with the latest scientific findings. To overcome this problem, we introduce a new task of disentangled paper summarization, which…

In this paper we consider error sums of the form \[\sum_{m=0}^{\infty} \varepsilon_m\Big( \,b_m\alpha - \frac{a_m}{c_m}\,\Big) \,,\] where $\alpha$ is a real number, $a_m$, $b_m$, $c_m$ are integers, and $\varepsilon_m=1$ or $\varepsilon_m…

The variational properties of the scalar so--called ``Universal'' equations are reviewed and generalised. In particular, we note that contrary to earlier claims, each member of the Euler hierarchy may have an explicit field dependence. The…

We define the generalized-Euler-constant function $\gamma(z)=\sum_{n=1}^{\infty} z^{n-1} (\frac{1}{n}-\log \frac{n+1}{n})$ when $|z|\leq 1$. Its values include both Euler's constant $\gamma=\gamma(1)$ and the "alternating Euler constant"…

This paper shows that finitely additive measures occur naturally in very general Divergence Theorems. The main results are two such theorems. The first proves the existence of pure normal measures for sets of finite perime- ter, which yield…

This tutorial provides a concise introduction to modern causal modeling by integrating potential outcomes and graphical methods. We motivate causal questions such as counterfactual reasoning under interventions and define binary treatments…

We develop a general framework to significantly reduce the degree of sum-of-squares proofs by introducing new variables. To illustrate the power of this framework, we use it to speed up previous algorithms based on sum-of-squares for two…

We introduce the notion of an approximation system as a generalization of Taylor approximation, and we give some first examples. Next we develop the general theory, including error bounds and a sufficient criterion for convergence. More…

This paper is an invitation to Fourier analysis in the context of reduced twisted C*-crossed products associated with discrete unital twisted C*-dynamical systems. We discuss norm-convergence of Fourier series, multipliers and summation…

In this thesis we show that the partial sums of the Maclaurin series for a certain class of entire functions possess scaling limits in various directions in the complex plane. In doing so we obtain information about the zeros of the partial…

In this second part of the paper, dedicated to theories with extra dimensions, a new physical notion about the "tensor length scale" is introduced, based on the gravitational theories with covariant and contravariant metric tensor…

This paper establishes an abstract Korovkin-type approximation theorem in general spaces, extending the framework of approximation theory to accommodate broader contexts. A critical result supporting this theorem is the proof that any…

In this paper we study the problem of computing wavelet coefficients of compactly supported functions from their Fourier samples. For this, we use the recently introduced framework of generalized sampling. Our first result demonstrates that…