Zobrazeno 1 - 10
of 34
pro vyhledávání: '"Ciosmak, Krzysztof J."'
Autor:
Ciosmak, Krzysztof J.
Let $X$ be a subset of a Hilbert space. We prove that if $v\colon X\to \mathbb{R}^m$ is such that \begin{equation*} \Big\lVert v(x)-\sum_{i=1}^m t_iv(x_i)\Big\rVert\leq \Big\lVert x-\sum_{i=1}^m t_ix_i\Big\rVert \end{equation*} for all $x,x_1,\dotsc,
Externí odkaz:
http://arxiv.org/abs/2402.14699
Autor:
Ciosmak, Krzysztof J.
We present a range of applications of localisation for constrained transports for pairs of probability measures in order with respect to a lattice cone. These examples comprise irreducible convex paving for martingale transports in infinite-dimension
Externí odkaz:
http://arxiv.org/abs/2312.13167
Autor:
Ciosmak, Krzysztof J.
We investigate an analogue of the irreducible convex paving in the context of generalised convexity. Consider two Radon probability measures $\mu,\nu$ ordered with respect to a cone $\mathcal{F}$ of functions on $\Omega$ stable under maxima. Under th
Externí odkaz:
http://arxiv.org/abs/2312.12281
Autor:
Ciosmak, Krzysztof J.
We demonstrate that the Cartan-Thullen theorem and its generalisation to the context of generalised convexity, which we establish herein, can be regarded as a consequence of the classical theorems of functional analysis. Furthermore, we characterise
Externí odkaz:
http://arxiv.org/abs/2307.04860
Autor:
Ciosmak, Krzysztof J.
We characterise equality cases in matrix H\"older's inequality and develop a divergence formulation of optimal transport of vector measures. As an application, we reprove the representation formula for measures in the polar cone to monotone maps. We
Externí odkaz:
http://arxiv.org/abs/2109.06588
Autor:
Ciosmak, Krzysztof J.
We develop and study a theory of optimal transport for vector measures. We resolve in the negative a conjecture of Klartag, that given a vector measure on Euclidean space with total mass zero, the mass of any transport set is again zero. We provide a
Externí odkaz:
http://arxiv.org/abs/2108.07201
Autor:
Ciosmak, Krzysztof J.
We partly extend the localisation technique from convex geometry to the multiple constraints setting. For a given $1$-Lipschitz map $u\colon\mathbb{R}^n\to\mathbb{R}^m$, $m\leq n$, we define and prove the existence of a partition of $\mathbb{R}^n$, u
Externí odkaz:
http://arxiv.org/abs/2108.07193
Autor:
Ciosmak, Krzysztof J.
We provide a unifying interpretation of various optimal transport problems as a minimisation of a linear functional over the set of all Choquet representations of a given pair of probability measures ordered with respect to a certain convex cone of f
Externí odkaz:
http://arxiv.org/abs/2001.11292
Autor:
Ciosmak, Krzysztof J.
For a given $1$-Lipschitz map $u\colon\mathbb{R}^n\to\mathbb{R}^m$ we define a partition, up to a set of Lebesgue measure zero, of $\mathbb{R}^n$ into maximal closed convex sets such that restriction of $u$ is an isometry on these sets. We consider a
Externí odkaz:
http://arxiv.org/abs/1905.02182
Autor:
Ciosmak, Krzysztof J.
We establish the sharp rate of continuity of extensions of $\mathbb{R}^m$-valued $1$-Lipschitz maps from a subset $A$ of $\mathbb{R}^n$ to a $1$-Lipschitz maps on $\mathbb{R}^n$. We consider several cases when there exists a $1$-Lipschitz extension w
Externí odkaz:
http://arxiv.org/abs/1904.02993