Related papers: Absolutely summing multilinear operators via inter…
The Bohnenblust-Hille inequality for $m$-linear forms was proven in 1931 as a generalization of the famous 4/3-Littlewood inequality. The optimal constants (or at least their asymptotic behavior as $m$ grows) is unknown, but significant for…
Recently, Dil and Boyadzhiev \cite{AD2015} proved an explicit formula for the sum of multiple harmonic numbers whose indices are the sequence $\left( {{{\left\{ 0 \right\}}_r},1} \right)$. In this paper we show that the sums of multiple…
A new family of generalized Pell numbers was recently introduced and studied by Br\'od \cite{Dorota}. These number possess, as Fibonacci numbers, a Binet formula. Using this, partial sums of arbitrary powers of generalized Pell numbers can…
In the space of holomorphic functions in a convex domain it is studied the interpolation problem by means of sums of the series of exponentials converging uniformly on all compact sets of the domain. The discrete set of the interpolation…
The Bohnenblust--Hille (polynomial and multilinear) inequalities were proved in 1931 in order to solve Bohr's absolute convergence problem on Dirichlet series. Since then these inequalities have found applications in various fields of…
A useful identity relating the infinite sum of two Bessel functions to their infinite integral was discovered in Dominici et al. (2012). Here, we extend this result to products of $N$ Bessel functions, and show it can be straightforwardly…
In the monograph Kounchev, O. I., Multivariate Polysplines. Applications to Numerical and Wavelet Analysis, Academic Press, San Diego-London, 2001, and in the paper Kounchev O., Render, H., Cardinal interpolation with polysplines on annuli,…
By using some techniques of the divided difference operators, we establish an 4n-point interpolation formula. Certain polynomials, such as Jackson's _8\phi_7 terminating summation formula, are special cases of this formula. Based on…
Let $d\geq 2$ and $k\geq 1$ be fixed. We prove that, for every $\epsilon>0$ and every real $\beta$, there exist integers $1\leq b_1,\ldots,b_k\leq N$ such that \[ \left\|\sum_{j=1}^k b_j^{1/d}-\beta\right\| \ll_{d,k,\epsilon}…
Two-point Feynman parameter integrals, with at most one mass and containing local operator insertions in $4+\ep$-dimensional Minkowski space, can be transformed to multi-integrals or multi-sums over hyperexponential and/or hypergeometric…
We present a new model-based interpolation procedure for satisfiability modulo theories (SMT). The procedure uses a new mode of interaction with the SMT solver that we call solving modulo a model. This either extends a given partial model…
In this note, we study the flint hills series of the form \begin{align} \sum \limits_{n=1}^{\infty}\frac{1}{(\sin^2n) n^3}\nonumber \end{align} via a certain method. The method essentially works by erecting certain pillars sufficiently…
We solve an interpolation problem for computing $\zeta(2n)$ in a rather elementary way, by generalizing the main idea in \cite{SE}.
We prove a general factorization theorem for Lipschitz summing operators in the context of metric spaces which recovers several linear and nonlinear factorization theorems that have been proved recently in different environments. New…
For any fixed $k\geq 2$, we prove that every sufficiently large integer can be expressed as the sum of a $k$th power of a prime and a number with at most $M(k)=6k$ prime factors. For sufficiently large $k$ we also show that one can take…
This paper introduces an interpolation-based method, called the reconstruction approach, for nonparametric regression. Based on the fact that interpolation usually has negligible errors compared to statistical estimation, the reconstruction…
We prove the version of interpolation theorem for non-commutative vector-valued fully symmetric spaces associated with fully symmetric Banach function spaces and a von Neumann algebra equipped with a faithful semifinite normal trace.
We consider a special class of binomial sums involving harmonic numbers and we prove three identities by using the elementary method of the partial fraction decomposition. Some applications to infinite series and congruences are given.
We consider a joint ordered multifactorisation for a given positive integer $n\geq 2$ into $m$ parts, where $n=n_1~\times~\ldots~\times~n_m$, and each part $n_j$ is split into one or more component factors. Our central result gives an…
We offer a proof of a summation formula equivalent to one due to Berndt. Our proof uses the M$\ddot{u}$ntz formula and the Poisson summation formula. By utilizing known properties of Mellin inversion, we give an example from a discontinuous…