Related papers: Existence Conditions for Dilation Families

In this article, the author proposes another way to define the completion of a metric space, which is different from the classical one via the dense property, and prove the equivalence between two definitions. This definition is based on…

This note presents a summary and review of various conditions and characterizations for matrix stability (in particular diagonal matrix stability) and matrix stabilizability.

In a metric space $M=(X,d)$, we say that $v$ is between $u$ and $w$ if $d(u,w)=d(u,v)+d(v,w)$. Taking all triples $\{u,v,w\}$ such that $v$ is between $u$ and $w$, one can associate a 3-uniform hypergraph with each finite metric space $M$.…

We prove several results of the following type: given finite dimensional normed space V there exists another space X with log (dim X) = O(log (dim V)) and such that every subspace (or quotient) of X, whose dimension is not "too small,"…

It is shown that separation conditions (separation curves) are fundamental objects of separability theory. They are used for the classification of certain clases of separable systems, for the proof of bi-Hamiltonian property and finally…

In this note we define summable families in tempered distribution spaces and we state some their properties and characterizations. Summable families are the analogous of summable sequences in separable Hilbert spaces, but in tempered…

In a space-time, a conformal structure is defined by the distribution of light-cones. Geodesics are traced by freely falling particles, and the collection of all unparameterized geodesics determines the projective structure of the…

In this paper we introduce a set of sufficient criteria for the construction of relative hemisystems of the Hermitian space $\mathrm{H}(3,q^2)$, unifying all known infinite families. We use these conditions to provide new proofs of the…

Given a family of model categories $\cal E \to \cal R$ over a Reedy category, we outline a set of conditions which lead to the existence of a Reedy model structure on the category of sections ${\sf Sect}(\cal R, \cal E)$. We prove that for…

We indicate how to construct a family of modulation function spaces that have a scaling symmetry. We also illustrate the behavior of the Schr\"odinger multiplier on such function spaces.

The aim of this paper is state of conditions that ensure the convexity of a Chebyshev sets in Hilbert spaces .

The aim of this paper is to prove all well-known metrization theorems using partitions of unity. To accomplish this, we first discuss sufficient and necessary conditions for existence of $\mathcal{U}$-small partitions of unity (partitions…

We establish two versions of a central theorem, the Family Colimit Theorem, for the coarse coherence property of metric spaces. This is a coarse geometric property and so is well-defined for finitely generated groups with word metrics. It…

In this paper, we present more regularity conditions which ensure the boundedness of dilation operators on Besov and Triebel-Lizorkin spaces equiped with general weights.

The paper concerns a new method to obtain a direct proof of the openness at linear rate/metric regularity of composite set-valued maps on metric spaces by the unification and refinement of several methods developed somehow separately in…

We consider a geometrization, i.e., we identify geometrical structures, for the space of density states of a quantum system. We also provide few comments on a possible application of this geometrization for composite systems.

A number of topics involving metrics and measures are discussed, including some of the special structure associated with ultrametrics.

Local unitary invariants allow one to test whether multipartite states are equivalent up to local basis changes. Equivalently, they specify the geometry of the "orbit space" obtained by factoring out local unitary action from the state…

This informal note provides some elementary examples to motivate the local structural results of [1] on the moduli space of genus one stable maps to projective space. The hope is that these examples will be helpful for graduate students to…

Most algorithms constructing bases of finite-dimensional vector spaces return basis vectors which, apart from orthogonality, do not show any special properties. While every basis is sufficient to define the vector space, not all bases are…