Related papers: A pasting lemma for Lipschitz functions

In 2002 F. Wirth has proved that the joint spectral radius of irreducible compact sets of matrices is locally Lipschitz continuous as a function of the matrix set. In the paper, an explicit formula for the related Lipschitz constant is…

A condition for the presence of a "gap" between symmetric spaces sufficient for the inclusion of one of these spaces into the other to be disjointly strictly singular is found. This condition is stated in terms of fundamental functions of…

The paper deals with the interplay between boundedness, order and ring structures in function lattices on the line and related metric spaces. It is shown that the lattice of all Lipschitz functions on a normed space $E$ is isomorphic to its…

We show that the de Rham Hilbert complex with mixed boundary conditions on bounded strong Lipschitz domains is closed and compact. The crucial results are compact embeddings which follow by abstract arguments using functional analysis…

Let Pi and Gamma be homogeneous Poisson point processes on a fixed set of finite volume. We prove a necessary and sufficient condition on the two intensities for the existence of a coupling of Pi and Gamma such that Gamma is a deterministic…

We give a very short proof of the fact that H1 functions on Lipschitz domains have L2 traces on the boundary of the domain.

Let $U \subseteq \mathbb C$ be bounded and open. For $0 < \alpha < 1$, $A_\alpha(U)$ is the set of functions in the little Lipschitz class with exponent $\alpha$ that are analytic in a neighborhood of $U$. We consider three conditions,…

We describe two distinct simple, short and self contained proofs of the composition lemma.

We propose a sufficient condition for invertibility of a polynomial mapping function defined on a cube or simplex. This condition is applicable to finite element analysis using curved meshes. The sufficient condition is based on an analysis…

Rademacher theorem states that every Lipschitz function on the Euclidean space is differentiable almost everywhere, where "almost everywhere" refers to the Lebesgue measure. In this paper we prove a differentiability result of similar type,…

We obtain a complete description of closed ideals in weighted Lipschitz algebras $\Lambda_\omega$ of analytic functions on the unit disk satisfying the following condition $$\frac{|f(z)-f(w)|}{\omega(|z-w|)}=o(1)\qquad(as |z-w|…

Using a modification of a generalized Takagi-van der Waerden function on a metric space we prove that for any closed subset of a metric space without isolated points there exists a continuous function such that its big and local Lipschitz…

We prove that an $\mathbb{R}$-action on a compact metric space embeds equivariantly in the space of one-Lipschitz functions $\mathbb{R}\to[0,1]$ if its fixed point set can be topologically embedded in the unit interval. This is a refinement…

We obtain necessary and sufficient conditions on a function in order that it be the Laplace transform of an absolutely monotonic function. Several closely related results are also given.

In this paper we study the existence of continuous solutions and their constructions for a second order iterative functional equation, which involves iterate of the unknown function and a nonlinear term. Imposing Lipschitz conditions to…

We give necessary and sufficient conditions for a pair of (generalized) functions $\rho_1(\mathbf{r}_1)$ and $\rho_2(\mathbf{r}_1,\mathbf{r}_2)$, $\mathbf{r}_i\in X$, to be the density and pair correlations of some point process in a…

We construct a Lipschitz truncation which approximates functions of bounded variation in the area-strict metric. The Lipschitz truncation changes the original function only on a small set similar to Lusin's theorem. Previous results could…

In this paper we prove the fundamental lemma for Deligne-Lusztig functions. Namely, for every Deligne-Lusztig function $\phi$ on a $p$-adic group $G$ we write down an explicit linear combination $\phi^H$ of Deligne-Lusztig functions on an…

We establish the sharp rate of continuity of extensions of $\mathbb{R}^m$-valued $1$-Lipschitz maps from a subset $A$ of $\mathbb{R}^n$ to a $1$-Lipschitz maps on $\mathbb{R}^n$. We consider several cases when there exists a $1$-Lipschitz…

We deal with a family of functionals depending on curvatures and we prove for them compactness and semicontinuity properties in the class of closed and bounded sets which satisfy a uniform exterior and interior sphere condition. We apply…