Related papers: Quiz your maths: do the uniformly continuous funct…
A set of all symmetric Banach function spaces defined on [0,1] is equipped with the partial order by the relation of continuous inclusion. Properties of symmetric spaces, which do not depend of their position in the ordered structure, are…
In these notes, we present a general result concerning the Lipschitz regularity of a certain type of set-valued maps often found in constrained optimization and control problems. The class of multifunctions examined in this paper is…
The Hurwitz space is a compactification of the space of rational functions of a given degree. We study the intersection of various strata of this space with its boundary. A study of the cohomology ring of the Hurwitz space then allows us to…
A normalized univalent function is uniformly convex if it maps every circular arc contained in the open unit disk with center in it into a convex curve. This article surveys recent results on the class of uniformly convex functions and on…
We study the space of bandlimited Lipschitz functions in one variable. In particular we provide a geometrical description of the natural interpolating and sampling sequences for this space. We also find a description of the trace of such…
We consider convex monotone $C_0$-semigroups on a Banach lattice, which is assumed to be a Riesz subspace of a $\sigma$-Dedekind complete Banach lattice. Typical examples include the space of all bounded uniformly continuous functions and…
The present paper is concerned with Lipschitz properties of convex mappings. One considers the general context of mappings defined on an open convex subset $\Omega$ of a locally convex space $X$ and taking values in a locally convex space…
For a finite lattice $\Lambda$, $\Lambda$-ultrametric spaces have, among other reasons, appeared as a means of constructing structures with lattices of equivalence relations embedding $\Lambda$. This makes use of an isomorphism of…
The similar sublattices of a planar lattice can be classified via its multiplier ring. The latter is the ring of rational integers in the generic case, and an order in an imaginary quadratic field otherwise. Several classes of examples are…
On a non-compact, smooth, connected, boundaryless, complete Riemannian manifold $(M,g)$, one can define its ideal boundary by rays (or equivalently, Busemann functions). From the viewpoint of Mather theory, boundary elements could be…
Here we consider a few topics related to Lipschitz classes for functions and curves in metric spaces.
We discuss the possibility to represent smooth nonnegative matrix-valued functions as finite linear combinations of fixed matrices with positive real-valued coefficients whose square roots are Lipschitz continuous. This issue is reduced to…
In this paper we apply ideas from the theory of Uniform Distribution of sequences to Functional Analysis and then drawing inspiration from the consequent results, we study concepts and results in Uniform Distribution itself. So let $E$ be a…
Given two compact sets, $E$ and $F$, on the unit circle, we study the class of subharmonic functions on the unit disk which can grow at the direction of $E$ and $F$ (sets of singularities) at different rate. The main result concerns the…
Consider the lattice of bounded linear operators on the space of Borel measures on a Polish space. We prove that the operators which are continuous with respect to the weak topology induced by the bounded measurable functions form a…
We find general conditions under which Lipschitz-free spaces over metric spaces are isomorphic to their infinite direct $\ell_1$-sum and exhibit several applications. As examples of such applications we have that Lipschitz-free spaces over…
We study the ring of polyfunctions over $\mathbb Z/n\mathbb Z$. The ring of polyfunctions over a commutative ring $R$ with unit element is the ring of functions $f:R\to R$ which admit a polynomial representative $p\in R[x]$ in the sense…
A study is made of linear isometries on Fr\'echet spaces for which the metric is given in terms of a sequence of seminorms. This establishes sufficient conditions on the growth of the function that defines the metric in terms of the…
This paper introduces the order-theoretic concept of lattices along with the concept of consistent quantification where lattice elements are mapped to real numbers in such a way that preserves some aspect of the order-theoretic structure.…
Given an F-sigma-delta subset A of the real line R of Lebesgue measure zero, we construct a monotone absolutely continuous function f from R to R such that the little Lipschitz constant of f is equal to infinity exactly at points of A.