Results 11 to 20 of about 62,718 (25)

The basic resolvents of position and momentum operators form a total set in the resolvent algebra [PDF]

arXiv, 2023
Let Q and P be the position and momentum operators of a particle in one dimension. It is shown that all compact operators can be approximated in norm by linear combinations of the basic resolvents (aQ + bP - i r)^{-1} for real constants a,b,r=/=0. This implies that the basic resolvents form a total set (norm dense span) in the C*-algebra R generated by
arxiv  

The resolving number of a graph [PDF]

arXiv, 2013
We study a graph parameter related to resolving sets and metric dimension, namely the resolving number, introduced by Chartrand, Poisson and Zhang. First, we establish an important difference between the two parameters: while computing the metric dimension of an arbitrary graph is known to be NP-hard, we show that the resolving number can be computed ...
arxiv  

Maker-Breaker resolving game [PDF]

arXiv, 2020
A set of vertices $W$ of a graph $G$ is a resolving set if every vertex of $G$ is uniquely determined by its vector of distances to $W$. In this paper, the Maker-Breaker resolving game is introduced. The game is played on a graph $G$ by Resolver and Spoiler who alternately select a vertex of $G$ not yet chosen.
arxiv  

Minimal resolving sets for the hypercube [PDF]

Graph Theory Notes of New York, vol. LXVII, pp. 50-53, November 2014, 2011
For a given undirected graph $G$, an \emph{ordered} subset $S = {s_1,s_2,...,s_k} \subseteq V$ of vertices is a resolving set for the graph if the vertices of the graph are distinguishable by their vector of distances to the vertices in $S$. While a superset of any resolving set is always a resolving set, a proper subset of a resolving set is not ...
arxiv  

On the generalized resolvent of linear pencils in Banach spaces [PDF]

arXiv, 2011
Utilizing the stability characterizations of generalized inverses of linear operator, we investigate the existence of generalized resolvents of linear pencils in Banach spaces. Some practical criterions for the existence of generalized resolvents of the linear pencil $\lambda\rightarrow T-\lambda S$ are provided and an explicit expression of the ...
arxiv  

A local directional growth estimate of the resolvent norm [PDF]

arXiv, 2018
We study the resolvent norm of a certain class of closed linear operators on a Hilbert space, including unbounded operators with compact resolvent. It is shown that for any point in the resolvent set there exist directions in which the norm grows at least quadratically with the distance from this point.
arxiv  

The Resolvent Average for Positive Semidefinite Matrices [PDF]

arXiv, 2009
We define a new average - termed the resolvent average - for positive semidefinite matrices. For positive definite matrices, the resolvent average enjoys self-duality and it interpolates between the harmonic and the arithmetic averages, which it approaches when taking appropriate limits. We compare the resolvent average to the geometric mean.
arxiv  

Channel Resolvability Using Multiplicative Weight Update Algorithm [PDF]

arXiv
We study the channel resolvability problem, which is used to prove strong converse of identification via channel. Channel resolvability has been solved by only random coding in the literature. We prove channel resolvability using the multiplicative weight update algorithm. This is the first approach to channel resolvability using non-random coding.
arxiv  

Variable-Length Resolvability for General Sources and Channels [PDF]

arXiv, 2017
We introduce the problem of variable-length source resolvability, where a given target probability distribution is approximated by encoding a variable-length uniform random number, and the asymptotically minimum average length rate of the uniform random numbers, called the (variable-length) resolvability, is investigated.
arxiv  

Nonlinear resolvents: distortion and order of starlikeness [PDF]

arXiv
This paper presents a new approach to studying nonlinear resolvents of holomorphically accretive mappings on the open unit ball of a complex Banach space. We establish a distortion theorem and apply it to address problems in geometric function theory concerning the class of resolvents.
arxiv