Results 101 to 110 of about 71,510 (217)

Local Hausdorff Measure

, 2016
A local Hausdorff dimension is defined on a metric space. We study its properties and use it to define a local Hausdorff measure. We show that in the case that in the local Hausdorff measure is finite we can recover the global Hausdorff dimension from the local one. Lastly, for a variable Ahlfors Q-regular measure on a compact metric space, we show the
openaire   +2 more sources

Fourier analytic properties of Kakeya sets in finite fields

Bulletin of the London Mathematical Society, Volume 58, Issue 5, May 2026.
Abstract We prove that a Kakeya set in a vector space over a finite field of size q$q$ always supports a probability measure, whose Fourier transform is bounded by q−1$q^{-1}$ for all non‐zero frequencies. We show that this bound is sharp in all dimensions at least 2.
Jonathan M. Fraser
wiley   +1 more source

Measure of noncompactness of operators and matrices on the spaces c and c0

International Journal of Mathematics and Mathematical Sciences, 2006
In this note, using the Hausdorff measure of noncompactness, necessary and sufficient conditions are formulated for a linear operator and matrices between the spaces c and c0 to be compact.
Bruno De Malafosse, Eberhard Malkowsky, Vladimir Rakocevic   +2 more
doaj   +1 more source

On planar self-similar sets with a dense set of rotations

, 2006
We prove that if $E$ is a planar self-similar set with similarity dimension $d$ whose defining maps generate a dense set of rotations, then the $d$-dimensional Hausdorff measure of the orthogonal projection of $E$ onto any line is zero.
Eroglu, Kemal Ilgar
core  

Cheeger's differentiation theorem via the multilinear Kakeya inequality

, 2019
Suppose that $(X,d,\mu)$ is a metric measure space of finite Hausdorff dimension and that, for every Lipschitz $f \colon X \to \mathbb R$, $\operatorname{Lip}(f,\cdot)$ is dominated by every upper gradient of $f$.
Bate, David, Kangasniemi, Ilmari, Orponen, Tuomas   +2 more
core  

The bounded variation capacity and Sobolev-type inequalities on Dirichlet spaces

Advances in Nonlinear Analysis
In this article, we consider the bounded variation capacity (BV capacity) and characterize the Sobolev-type inequalities related to BV functions in a general framework of strictly local Dirichlet spaces with a doubling measure via the BV capacity.
Xie Xiangyun, Liu Yu, Li Pengtao, Huang Jizheng   +3 more
doaj   +1 more source

Gromov - Hausdorff Convergence and Topological Stability for Actions on Wasserstein Hyperspaces

Journal of Applied Sciences and Environmental Management
In this paper, we make use of topological stability from Gromov – Hausdorff view point to establish the Gromov – Hausdorff convergence and stability of induced actions on Wasserstein hyperspaces between maps.
M. A. Morawo, M. L. Danyaro, A. S. Bailey, K. Y. Azeez   +3 more
doaj  

Neutral functional differential equations of second-order with infinite delays

Electronic Journal of Differential Equations, 2010
This work shows the existence of mild solutions to neutral functional differential equations of second-order with infinite delay. The Hausdorff measure of noncompactness and fixed point theorem are used, without assuming compactness on the associated
Runping Ye, Guowei Zhang
doaj  

Controllability of nonlinear differential evolution systems in a separable Banach space

Electronic Journal of Differential Equations, 2012
In this article, we study the controllability of semilinear evolution differential systems with nonlocal initial conditions in a separable Banach space. The results are obtained by using Hausdorff measure of noncompactness and a new calculation method.
Bheeman Radhakrishnan, Krishnan Balachandran   +1 more
doaj  

Stress relaxation constitutive model of rock based on Hausdorff derivative. [PDF]

PLoS One
Li Y.
europepmc   +1 more source