Related papers: Analytic functions in shift-invariant spaces and a…

In this survey, we consider Banach spaces of analytic functions in one and several complex variables for which: (i) polynomials are dense, (ii) point-evaluations on the domain are bounded linear functionals, and (iii) the shift operator…

In this paper, we introduce a method of converting implicit equations to the usual forms of functions locally without differentiability. For a system of implicit equations which are equipped with continuous functions, if there are unique…

The paper is devoted to developing subdifferential theory for set-valued mappings taking values in ordered infinite-dimensional spaces. This study is motivated by applications to problems of vector and set optimization with various…

This paper develops a functional-analytic framework for approximating the push-forward induced by an analytic map from finitely many samples. Instead of working directly with the map, we study the push-forward on the space of locally…

Let $L$ be a proper differentiation invariant subspace of $C^\infty(a,b)$ such that the restriction operator $\frac{d}{dx}\bigl{|}_L$ has a discrete spectrum $\Lambda$ (counting with multiplicities). We prove that $L$ is spanned by…

We define a number of natural (from geometric and combinatorial points of view) deformation spaces of valuations on finite graphs, and study functions over these deformation spaces. These functions include both direct metric invariants…

Polynomial invariants are fundamental objects in analysis on Lie groups and symmetric spaces. Invariant differential operators on symmetric spaces are described by Weyl group invariant polynomial. In this article we give a simple criterion…

We investigate the existence of subinvariant metric functionals for commuting families of nonexpansive mappings in noncompact subsets of Banach spaces. Our findings underscore the practicality of metric functionals when searching for fixed…

We construct valuations on the space of finite-valued convex functions using integration of differential forms over the differential cycle associated to a convex function. We describe the kernel of this procedure and show that the…

We present large sample results for partitioning-based least squares nonparametric regression, a popular method for approximating conditional expectation functions in statistics, econometrics, and machine learning. First, we obtain a…

We show that unary log-analytic functions are polynomially bounded. In the higher dimensional case globally a log-analytic function can have exponential growth. We show that a log-analytic function is polynomially bounded on a definable set…

Motivated by classical results for Gevrey spaces and their applications to nonlinear partial differential equations we define so-called Gevrey-modulation spaces. We establish analytic as well as non-analytic superposition results on…

We prove some sharp extremal distance results for functions in weighted Bergman spaces on the upper halfplane.We also prove such results in the context of bounded strictly pseudoconvex domains with smooth boundary

The set of matrix tuples with invariant subspaces whose dimensions sum up to the dimension of the space, but which do not span the whole space form an algebraic hypersurface. We found the equation of this hypersurface. This generalizes…

Valuations on the space of finite-valued convex functions on $\mathbb{C}^n$ that are continuous, dually epi-translation invariant, as well as $\mathrm{U}(n)$-invariant are completely classified. It is shown that the space of these…

We introduce a novel type of approximation spaces for functions with values in a nonlinear manifold. The discrete functions are constructed by piecewise polynomial interpolation in a Euclidean embedding space, and then projecting pointwise…

We prove that every continuous function $f:E\to Y$ depends on countably many coordinates, if $E$ is an $(\aleph_1,\aleph_0)$-invariant pseudo-$\aleph_1$-compact subspace of a product of topological spaces and $Y$ is a space with a regular…

We consider approximation by functions with finite support and characterize its approximation spaces in terms of interpolation spaces and Lorentz spaces.

In this paper we characterize the closed invariant subspaces for the ($*$-)multiplier operator of the quaternionic space of slice $L^2$ functions. As a consequence, we obtain the inner-outer factorization theorem for the quaternionic Hardy…

Input-affine dynamical systems often arise in control and modeling scenarios, such as the data-driven case when state-derivative observations are recorded under bounded noise. Common tasks in system analysis and control include optimal…