Zobrazeno 1 - 10
of 49
pro vyhledávání: '"Roysdon, Michael"'
An affine P\'olya-Szeg\"o principle for a family of affine energies, with equality condition characterization, is demonstrated. In particular, this recovers, as special cases, the $L^p$ affine P\'olya-Szeg\"o principles due to Cianchi, Lutwak, Yang a
Externí odkaz:
http://arxiv.org/abs/2409.02232
Autor:
Hoehner, Steven, Roysdon, Michael
A new position is introduced and studied for the convolution of log-concave functions, which may be regarded as a functional analogue of the maximum intersection position of convex bodies introduced and studied by Artstein-Avidan and Katzin (2018) an
Externí odkaz:
http://arxiv.org/abs/2401.01033
Given two non-negative functions $f$ and $g$ such that the Radon transform of $f$ is pointwise smaller than the Radon transform of $g$, does it follow that the $L^p$-norm of $f$ is smaller than the $L^p$-norm of $g$ for a given $p>0$? We consider thi
Externí odkaz:
http://arxiv.org/abs/2305.17796
Publikováno v:
Journal of Functional Analysis, 2024, ISSN 0022-1236
Schneider introduced an inter-dimensional difference body operator on convex bodies and proved an associated inequality. In the prequel to this work, we showed that this concept can be extended to a rich class of operators from convex geometry and pr
Externí odkaz:
http://arxiv.org/abs/2305.17468
For a convex body $K$ in $\mathbb R^n$, the inequalities of Rogers-Shephard and Zhang, written succinctly, are $$\text{vol}_n(DK)\leq \binom{2n}{n} \text{vol}_n(K) \leq \text{vol}_n(n\text{vol}_n(K)\Pi^\circ K).$$ Here, $DK=\{x\in\mathbb R^n:K\cap(K+
Externí odkaz:
http://arxiv.org/abs/2305.00479
In 1970, Schneider generalized the difference body of a convex body to higher-order, and also established the higher-order analogue of the Rogers-Shephard inequality. In this paper, we extend this idea to the projection body, centroid body, and radia
Externí odkaz:
http://arxiv.org/abs/2304.07859
Autor:
Roysdon, Michael, Xing, Sudan
We construct the extension of the curvilinear summation for bounded Borel measurable sets to the $L_p$ space for multiple power parameter $\bar{\alpha}=(\alpha_1, \cdots, \alpha_{n+1})$ when $p>0$. Based on this $L_{p,\bar{\alpha}}$-curvilinear summa
Externí odkaz:
http://arxiv.org/abs/2209.03104
Publikováno v:
In Journal of Functional Analysis 15 January 2025 288(2)
An asymptotic formula is proved for the expected $T$-functional of the convex hull of independent and identically distributed random points sampled from the Euclidean unit sphere in $\mathbb{R}^n$ according to an arbitrary positive continuous density
Externí odkaz:
http://arxiv.org/abs/2202.01353
Autor:
Roysdon, Michael A.
This dissertation concerns geometric and functional inequalities arising in the areas of convex geometry, asymptotic geometric analysis, and measure theory.