Related papers: Functional analysis in asymmetric normed spaces

Recently a new approach to varying exponent $L^{p(\cdot)}$ space norms employing weak solutions to first order ordinary differential equations was initiated by the author. The duality of these ODE-determined $L^{p(\cdot)}$ spaces is…

We discuss non-commutative field theories in coordinate space. To do so we introduce pseudo-localized operators that represent interesting position dependent (gauge invariant) observables. The formalism may be applied to arbitrary field…

We discuss topological versions of the closed graph theorem, where continuity is inferred from near continuity in tandem with suitable conditions on source or target spaces. We seek internal characterizations of spaces satisfying a closed…

In [1] we introduced the concept of structured space, which is a topological space that locally resembles some algebraic structures. In [2] we proceeded the study of these spaces, developing two cohomology theories. The aim of this paper is…

We revisit the classical problem of comparing regression functions, a fundamental question in statistical inference with broad relevance to modern applications such as data integration, transfer learning, and causal inference. Existing…

There are several examples of spaces of univariate functions for which we have a characterization of all sets of knots which are poised for the interpolation problem. For the standard spaces of univariate polynomials, or spline functions…

We evaluate the shattering dimension of various classes of linear functionals on various symmetric convex sets. The proofs here relay mostly on methods from the local theory of normed spaces and include volume estimates, factorization…

Using tools provided by the theory of abstract convexity, we extend conditions for zero duality gap to the context of nonconvex and nonsmooth optimization. Mimicking the classical setting, an abstract convex function is the upper envelope…

The study of convex functions - in particular, of their optimization (really minimization) is one of the most important fields of applied mathematics. Convexity seems to be one of those incredibly well-chosen hypotheses which is just…

There are several notions of duality between lines and points. In this note, it is shown that all these can be studied in a unified way. Most interesting properties are independent of specific choices. It is also shown that either dual…

This article studies problems of optimal transport, by embedding them in a general functional analytic framework of convex optimization. This provides a unified treatment of a large class of related problems in probability theory and allows…

It is the purpose of this article to compare various concepts of ``function spaces''. In particular we compare notions of the concept of Banach Function Spaces (in the spirit of Luxemburg-Zaanen) to the setting of solid BF-spaces as it is…

Spectral Barron spaces, constituting a specialized class of function spaces that serve as an interdisciplinary bridge between mathematical analysis, partial differential equations (PDEs), and machine learning, are distinguished by the decay…

Starting from a description of various generalized function algebras based on sequence spaces, we develop the general framework for considering linear problems with singular coefficients or non linear problems. Therefore, we prove…

In this paper we review some connections between harmonic analysis and the modern theory of automorphic forms. We indicate in some examples how the study of problems of harmonic analysis brings us to the important objects of the theory of…

In this article we develop a duality principle suitable for a large class of problems in optimization. The main result is obtained through basic tools of convex analysis and duality theory. We establish a correct relation between the…

Statistical depth functions provide measures of the outlyingness, or centrality, of the elements of a space with respect to a distribution. It is a nonparametric concept applicable to spaces of any dimension, for instance, multivariate and…

We consider a class of weighted harmonic functions in the open upper half-plane known as $\alpha$-harmonic functions. Of particular interest is the uniqueness problem for such functions subject to a vanishing Dirichlet boundary value on the…

We consider various inequalities for polynomials, with an emphasis on the most fundamental inequalities of approximation theory. In the sequel a key role is played by the generalized Minkowski functional \alpha(K,x), already being used by…

: In studies of discrete structures, functions are frequently used that express proximity, but are not metrics. We consider a class of such functions that is characterized by a normalization condition and an inequality that plays the same…