Related papers: Rigidity of bi-Lipschitz equivalence of weighted h…

Various convergence results for the Bergman kernel of the Hilbert space of all polynomials in \C^{n} of total degree at most k, equipped with a weighted norm, are obtained. The weight function is assumed to be C^{1,1}, i.e. it is…

We give a complete description of homomorphisms between two Banach algebras of Lipschitz functions with values in continuous functions. We also characterize the compactness of those homomorphisms.

In the article the necessary and sufficient conditions for a representation of Lipschitz function of two variables as a difference of two convex functions are formulated. An algorithm of this representation is given. The outcome of this…

We study the ambient Lipschitz geometry of semialgebraic surfaces. It was discovered in \cite{BBG} that ambient Lipschitz Geometry is different from the outer Lipschtz geometry. We show that two surface germs in $\mathbb{R}^3$, Lipschitz…

In this paper, we introduce a new bi-Lipschitz invariant for analytic function germs in two variables, enhancing the Henry-Parusinski invariant.

We show that for a weighted Lipschitz operator $\omega\widehat{f}$, certain linear properties are equivalent. Specifically, we prove that compactness, strict singularity, and strict cosingularity are all equivalent to the property of not…

We extend the duality principle for the $\Gamma$-convergence of convex lower semicontinuous functions, which was previously established only in separable reflexive Banach spaces, to the broader class of weakly compactly generated (WCG)…

We show that, for all $\alpha\geq 0$, the generalized Grushin plane $\mathbb{G}_{\alpha}$ is bi-Lipschitz homeomorphic to a $2$-dimensional quasiplane in the Euclidean space $\mathbb{R}^{[\alpha ]+2}$, where $[\alpha]$ is the integer part…

Motivated by applications for simulating quantum many body functions, we propose a new universal ansatz for approximating anti-symmetric functions. The main advantage of this ansatz over previous alternatives is that it is bi-Lipschitz with…

Let $\Omega$ be a domain in $\Ri^d$ with boundary $\Gamma$${\!,}$ $d_\Gamma$ the Euclidean distance to the boundary and $H=-\divv(C\,\nabla)$ an elliptic operator with $C=(\,c_{kl}\,)>0$ where $c_{kl}=c_{lk}$ are real, bounded, Lipschitz…

The main goal of this paper is to show that if a real valued function defined on a groupoid satisfies a certain Levi--Civita-type functional equation, then it also fulfills a Cauchy--Schwarz-type functional inequality. In particular, if the…

We show that two families of germs of real-analytic subsets in $C^{n}$ are formally equivalent if and only if they are equivalent of any finite order. We further apply the same technique to obtain analogous statements for equivalences of…

The aim of this paper is to consider the relation between Lie-isoclinism and isomorphism of two pairs of Leibniz algebras. We show that, unlike the absolute case for finite dimensional Lie algebras, these concepts are not identical, even if…

Two semisimple algebraic groups of the same type are said to be motivic equivalent if the motives of the associated projective homogeneous varieties of the same type are isomorphic. We give general criteria of motivic equivalence in terms…

We solve two main questions on linear structures of (non-)norm-attaining Lipschitz functions. First, we show that for every infinite metric space $M$, the set consisting of Lipschitz functions on $M$ which do not strongly attain their norm…

A C*-metric algebra consists of a unital C*-algebra and a Leibniz Lip-norm on the C*-algebra. We show that if the Lip-norms concerned are lower semicontinuous, then any unital *-homomorphism from a C*-metric algebra to another one is…

The main purpose of this paper is to develop some methods to investigate equivalent norms and Hardy-Littlewood type Theorems on Lipschitz type spaces of analytic functions and complex-valued harmonic functions. Initially, some…

We prove that any complex or real analytic set or function germ is topologically equivalent to a germ defined by polynomial equations whose coefficients are algebraic numbers.

It is shown that, generically, a positive continuous functions cannot be written as the derivative of a bi-Lipschitz plane homeomorphism. The same is proved for generic bounded functions.

Let K be a p-adic field, and suppose that f and g are germs of analytic functions on K which are tangent to the identity at 0. It is known that f and g are homeomorphically equivalent, meaning there is an invertible germ h conjugating f to…