Zobrazeno 1 - 10
of 149
pro vyhledávání: '"Doust, Ian"'
Autor:
Doust, Ian, Weston, Anthony
Associated to any finite metric space are a large number of objects and quantities which provide some degree of structural or geometric information about the space. In this paper we show that in the setting of subsets of weighted Hamming cubes there
Externí odkaz:
http://arxiv.org/abs/2404.06684
Autor:
Doust, Ian, Weston, Anthony
Nontrivial $p$-polygonal equalities impose certain conditions on the geometry of a metric space $(X,d)$ and so it is of interest to be able to identify the values of $p \in [0,\infty)$ for which such equalities exist. Following work of Li and Weston,
Externí odkaz:
http://arxiv.org/abs/2404.06658
Autor:
Doust, Ian, Stoneham, Alan
It is an open problem whether one can always extend an absolutely continuous function (in the sense of Ashton and Doust) on a compact subset of the plane to a larger compact set. In this paper we show that this can be done for a large family of initi
Externí odkaz:
http://arxiv.org/abs/2308.04628
Autor:
Blower, Gordon, Doust, Ian
Publikováno v:
J. Math. Anal. Appl., 525 (2023), Paper 127140, 24pp
Let $(-A,B,C)$ be a linear system in continuous time $t>0$ with input and output space ${\mathbb C}^2$ and state space $H$. The scattering functions $\phi_{(x)}(t)=Ce^{-(t+2x)A}B$ determines a Hankel integral operator $\Gamma_{\phi_{(x)}}$; if $\Gamm
Externí odkaz:
http://arxiv.org/abs/2210.07086
Publikováno v:
Results Math., 78 (2023) Paper 20, 34pp
The spaces $BV(\sigma)$ and $AC(\sigma)$ were introduced as part of a program to find a general theory which covers both well-bounded operators and trigonometrically well-bounded operators acting on a Banach space. Since their initial appearance it h
Externí odkaz:
http://arxiv.org/abs/2206.00986
Autor:
Doust, Ian, Wolf, Reinhard
Publikováno v:
Proc. Amer. Math. Soc. Ser. B, 9 (2022) 125-134
Let $D$ denote the distance matrix for an $n+1$ point metric space $(X,d)$. In the case that $X$ is an unweighted metric tree, the sum of the entries in $D^{-1}$ is always equal to $2/n$. Such trees can be considered as affinely independent subsets o
Externí odkaz:
http://arxiv.org/abs/2109.07052
Publikováno v:
J. Funct. Anal. 281 (2021) 109230
The maximal roundness of a metric space is a quantity that arose in the study of embeddings and renormings. In the setting of Banach spaces, it was shown by Enflo that roundness takes on a much simpler form. In this paper we provide simple computatio
Externí odkaz:
http://arxiv.org/abs/2105.13739
Autor:
Al-shakarchi, Shaymaa, Doust, Ian
Publikováno v:
Oper. Matrices 15 (2021), no. 4, 1581-1596
In this paper we investigate the relationship between the properties of a compact set $\sigma \subseteq \mathbb{C}$ and the structure of the space $BV(\sigma)$ of functions of bounded variation (in the sense of Ashton and Doust) defined on $\sigma$.
Externí odkaz:
http://arxiv.org/abs/2007.05701
Autor:
Al-shakarchi, Shaymaa, Doust, Ian
Publikováno v:
Banach J. Math. Anal., 15, 31 (2021)
For certain families of compact subsets of the plane, the isomorphism class of the algebra of absolutely continuous functions on a set is completely determined by the homeomorphism class of the set. This is analogous to the Gelfand--Kolmogorov theore
Externí odkaz:
http://arxiv.org/abs/2007.05702
Graham and Winkler derived a formula for the determinant of the distance matrix of a full-dimensional set of $n + 1$ points $\{ x_{0}, x_{1}, \ldots , x_{n} \}$ in the Hamming cube $H_{n} = ( \{ 0,1 \}^{n}, \ell_{1} )$. In this article we derive a fo
Externí odkaz:
http://arxiv.org/abs/2005.09205