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We obtain an explicit characterization of the $K$-functional of a pair of weighted classical Lorentz spaces of type $S$. We develop a method for obtaining such characterization based on a relation between the desired quantity and the…

Functional Analysis · Mathematics 2025-12-30 Amiran Gogatishvili , Julio S. Neves , Luboš Pick , Hana Turčinová

We detail how to use Newton's method for distortion-based curved $r$-adaption to a discrete high-order metric field while matching a target geometry. Specifically, we combine two terms: a distortion measuring the deviation from the target…

Computational Engineering, Finance, and Science · Computer Science 2023-03-22 Guillermo Aparicio-Estrems , Abel Gargallo-Peiró , Xevi Roca

A new application of subspaces interpolation for the construction of nonlinear Parametric Reduced Order Models (PROMs) is proposed. This approach is based upon the Riemannian geometry of the manifold formed by the quotient of the set of…

Numerical Analysis · Mathematics 2020-09-25 M. Oulghelou , C. Allery

We study a new bi-Lipschitz invariant \lambda(M) of a metric space M; its finiteness means that Lipschitz functions on an arbitrary subset of M can be linearly extended to functions on M whose Lipschitz constants are enlarged by a factor…

Metric Geometry · Mathematics 2007-05-23 A. Brudnyi , Yu. Brudnyi

The aim of this paper is to characterize universal and multiplier interpolating sequences for de Branges-Rovnyak spaces H (b) where the defining function b is a general non-extreme rational function. Our results carry over to recently…

Complex Variables · Mathematics 2025-12-11 Andreas Hartmann , Giuseppe Lamberti

Motivated by recent applications of weighted norm inequalities to maximal regularity of first and second order Cauchy problems, we study real interpolation spaces on the basis of general Banach function spaces and, in particular, weighted…

Functional Analysis · Mathematics 2016-01-11 Ralph Chill , Sebastian Krol

The extension of the concept of $p-$summability for linear operators to the context of Lipschitz operators on metric spaces has been extensively studied in recent years. This research primarily uses the linearization of the metric space $M$…

Functional Analysis · Mathematics 2024-10-29 R. Arnau , E. A. Sánchez Pérez , S. Sanjuan

In this paper, we discuss a novel model reduction framework for generalized linear systems. The transfer functions of these systems are assumed to have a special structure, e.g., coming from second-order linear systems and time-delay…

Numerical Analysis · Mathematics 2019-10-31 Peter Benner , Pawan Goyal , Igor Pontes Duff

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…

Machine Learning · Statistics 2019-11-28 Shifeng Xiong

Interpolation Theory gives techniques for constructing spaces from two initial Banach spaces. We provide several conditions under which the restriction of a holomorphic map $f:X_0+X_1 \rightarrow Y_0+Y_1$ to the interpolated spaces (using…

Functional Analysis · Mathematics 2017-06-21 Pablo Jiménez-Rodíguez

The paper introduces the class of O-metric spaces, a novel generalization of metric-type spaces, classifying almost all possible metric types into upward and downward O-metrics. We list some topologies arising from O-metrics and discuss…

General Mathematics · Mathematics 2025-04-29 Hallowed O. Olaoluwa , Aminat O. Ige , Johnson O. Olaleru

In the paper Description of the $K$-spaces by means of $J$-spaces and the reverse problem, Math. Nachr. 296 (2023), no. 9, 4002--4031, we have establish conditions under which the limiting $K$-space $(X_0,X_1)_{0,q,b;K}$, involving a slowly…

Functional Analysis · Mathematics 2025-01-16 Bohumír Opic , Manvi Grover

We give a complete characterization of limiting interpolation spa\-ces for the real method of interpolation using extrapolation theory. For this purpose the usual tools (e.g., Boyd indices or the boundedness of Hardy type operators) are not…

Functional Analysis · Mathematics 2018-09-05 Sergey V. Astashkin , Konstantin V. Lykov , Mario Milman

Let $\mathcal{M}$ be a semifinite von Neumann algebra. We equip the associated noncommutative $L_p$-spaces with their natural operator space structure introduced by Pisier via complex interpolation. On the other hand, for $1<p<\infty$ let…

Operator Algebras · Mathematics 2021-09-15 Marius Junge , Quanhua Xu

We give sufficient conditions for a metric space to bilipschitz embed in L_1. In particular, if X is a length space and there is a Lipschitz map u:X--->R such that for every interval I in R, the connected components of the inverse image…

Metric Geometry · Mathematics 2011-10-12 Jeff Cheeger , Bruce Kleiner

In a previous paper the authors developed a H^1-BMO theory for unbounded metric measure spaces $(M,\rho,m)$ of infinite measure that are locally doubling and satisfy two geometric properties, called "approximate midpoint" property and…

Functional Analysis · Mathematics 2008-11-04 A. Carbonaro , G. Mauceri , S. Meda

For nonlinear reduced-order models, especially for those with non-polynomial nonlinearities, the computational complexity still depends on the dimension of the original dynamical system. As a result, the reduced-order model loses its…

Numerical Analysis · Mathematics 2013-04-30 Zhu Wang

We present a novel projection-based model reduction framework for parametric linear time-invariant systems that allows interpolating the transfer function at a given frequency point along parameter-dependent curves as opposed to the…

Numerical Analysis · Mathematics 2021-04-05 Ion Victor Gosea , Serkan Gugercin , Benjamin Unger

A metric space $X$ is {\em injective} if every non-expanding map $f:B\to X$ defined on a subspace $B$ of a metric space $A$ can be extended to a non-expanding map $\bar f:A\to X$. We prove that a metric space $X$ is a Lipschitz image of an…

General Topology · Mathematics 2024-05-28 Judyta Bąk , Taras Banakh , Joanna Garbulińska-Węgrzyn , Magdalena Nowak , Michał Popławski

We define a conforming B-spline discretisation of the de Rham complex on multipatch geometries. We introduce and analyse the properties of interpolation operators onto these spaces which commute w.r.t. the surface differential operators.…

Numerical Analysis · Mathematics 2019-06-28 Annalisa Buffa , Jürgen Dölz , Stefan Kurz , Sebastian Schöps , Rafael Vázques , Felix Wolf