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In the last two decades, considerable research has been devoted to a phenomenon known as spatial confounding. Spatial confounding is thought to occur when there is multicollinearity between a covariate and the random effect in a spatial…
We characterize noncommutative symmetric Banach spaces for which every bounded sequence admits either a convergent subsequence, or a $2$-co-lacunary subsequence. This extends the classical characterization, due to R\"abiger.
We decompose a matrix Y into a sum of bilinear terms in a stepwise manner, by considering Y as a mapping from a finite dimensional Banach space into another finite dimensional Banach space. We provide transition formulas, and represent them…
In this article, we investigate nonlinear metric subregularity properties of set-valued mappings between general metric or Banach spaces. We demonstrate that these properties can be treated in the framework of the theory of (linear) error…
We give a direct proof of the fact that a quasi-Banach space coarsely embeds into a Hilbert space if and only if it uniformly embeds into a Hilbert space.
In this paper, the convergence of alternating minimization is established for non-smooth convex optimization in Banach spaces, and novel rates of convergence are provided. As objective function a composition of a smooth and a non-smooth…
We perform certain alternating binomial summations with parameters that occur in the analysis of algorithms. A combination of integral and special function and special number representations is used. The results are sufficiently general to…
In this article, we first try to make the known analogy between convexity and plurisubharmonicity more precise. Then we introduce a notion of strict plurisubharmonicity analogous to strict convexity, and we show how this notion can be used…
In the nonlinear geometry of Banach spaces where the objects in the category are Banach spaces as in the linear case, the morphisms in the new setting are taken to comprise of certain nonlinear maps involving say, Lipschitz maps and, in…
The spatial distribution has been widely used to develop various nonparametric procedures for finite dimensional multivariate data. In this paper, we investigate the concept of spatial distribution for data in infinite dimensional Banach…
Computing modular coincidences can show whether a given substitution system, which is supported on a point lattice in R^d, consists of model sets or not. We prove the computatibility of this problem and determine an upper bound for the…
We continue to investigate cases when the Repov\v{s}-Semenov splitting problem for selections has an affirmative solution for continuous set-valued mappings. We consider the situation in infinite-dimensional uniformly convex Banach spaces.…
The aim of this paper is to establish a strong convergence theorem for a strongly nonexpansive sequence in a Banach space. We also deal with some applications of the convergence theorem.
In this article on variational regularization for ill-posed nonlinear problems, we are once again discussing the consequences of an oversmoothing penalty term. This means in our model that the searched-for solution of the considered…
We show in this paper that every bijective linear isometry between the continuous section spaces of two non-square Banach bundles gives rise to a Banach bundle isomorphism. This is to support our expectation that the geometric structure of…
Given an infinite matrix $M=(m_{nk})$ we study a family of sequence spaces $\ell_M^p$ associated with it. When equipped with a suitable norm $\|\cdot\|_{M,p}$ we prove some basic properties of the Banach spaces of sequences…
This note extends a recent result of Mendelson on the supremum of a quadratic process to squared norms of functions taking values in a Banach space. Our method of proof is a reduction by a symmetrization argument and observation about the…
We study the obstructions to coarse universality in separable dual Banach spaces. We prove coarse non-universality of several classes of dual spaces, including those with conditional spreading bases, as well as generalized James and James…
In this paper, we introduce the notion of topologically Banach contraction mapping defined on an arbitrary topological space X with the help of a continuous function $g:X\times X\rightarrow \mathbb{R}$ and investigate the existence of fixed…
In this paper we provide necessary and sufficient conditions for the existence of the Kurzweil, McShane and Riemann product integrals of step mappings with well-ordered steps, and for right regulated mappings with values in Banach algebras.…