Related papers: A method of induction the distances with Hilbert s…
Isomorphisms of separable Hilbert spaces are analogous to isomorphisms of n-dimensional vector spaces. However, while n-dimensional spaces in applications are always realized as the Euclidean space R^n, Hilbert spaces admit various useful…
We prove that the L^2 Riemannian metric on the manifold of all smooth Riemannian metrics on a fixed closed, finite-dimensional manifold induces a metric space structure. As the L^2 metric is a weak Riemannian metric, this fact does not…
We investigate the relation between weighted quasi-metric Spaces and Finsler Spaces. We show that the induced metric of a Randers space with reversible geodesics is a weighted quasi-metric space.
We prove the Invariant Subspace Conjecture for separable Hilbert spaces.
We give some fundamental properties of the induced structures on submanifolds immersed in almost product or locally product Riemannian manifolds. We study the induced structure by the composition of two isometric immersions on submanifolds…
This paper presents a data structure that summarizes distances between configurations across a robot configuration space, using a binary space partition whose cells contain parameters used for a locally linear approximation of the distance…
The aim of this article is to define and compare several distances (or metrics) between operators acting on different (separable) Hilbert spaces. We consider here three main cases of how to measure the distance between two bounded…
A description of the real, complete modules over the Clifford algebra of a Hilbert space, with the elements of the latter acting by skew-symmetric operators.
In this paper we continue the study of dilatation structures, introduced in math.MG/0608536 . A dilatation structure on a metric space is a kind of enhanced self-similarity. By way of examples this is explained here with the help of the…
We develop an alternative description of the procedure of vertical integration based on the observation that amplitudes can be written in BRST exact form in the large Hilbert space. We relate this approach to the description of vertical…
The Hilbert scheme $S^{[n]}$ of points on an algebraic surface $S$ is a simple example of a moduli space and also a nice (crepant) resolution of singularities of the symmetric power $S^{(n)}$. For many phenomena expected for moduli spaces…
We propose a variable metric forward-backward splitting algorithm and prove its convergence in real Hilbert spaces. We then use this framework to derive primal-dual splitting algorithms for solving various classes of monotone inclusions in…
We introduce the notion of coarse metric. Every coarse metric induces a coarse structure on the underlying set. Conversely, we observe that all coarse spaces come from a particular type of coarse metric in a unique way. In the case when the…
An isometric embedding of a graph into a metric space is an embedding of the vertices such that the smallest number of edges connecting any two vertices equals to the distance in the metric space between the images. In this paper, we study…
Consider the quotient of a Hilbert space by a subgroup of its automorphisms. We study whether this orbit space can be embedded into a Hilbert space by a bilipschitz map, and we identify constraints on such embeddings.
Recently, the theory of symmetric spaces has come to play an increased role in the physics of integrable systems and in quantum transport problems. In addition, it provides a classification of random matrix theories. In this paper we give a…
The Hilbert metric between two points $x,y$ in a bounded convex domain $G$ is defined as the logarithm of the cross-ratio of $x,y$ and the intersection points of the Euclidean line passing through the points $x,y$ and the boundary of the…
Theoretical studies have proven that the Hilbert space has remarkable performance in many fields of applications. Frames in tensor product of Hilbert spaces were introduced to generalize the inner product to high-order tensors. However,…
Finite metric spaces arise in many different contexts. Enormous bodies of data, scientific, commercial and others can often be viewed as large metric spaces. It turns out that the metric of graphs reveals a lot of interesting information.…
This paper proposes a new distance metric between clusterings that incorporates information about the spatial distribution of points and clusters. Our approach builds on the idea of a Hilbert space-based representation of clusters as a…