Zobrazeno 1 - 10
of 40
pro vyhledávání: '"PALSSON, EYVINDUR ARI"'
We introduce a class of Falconer distance problems, which we call of restricted type, lying between the classical version and its pinned variant. Prototypical restricted distance sets are the diagonal distance sets, $k$-point configuration sets given
Externí odkaz:
http://arxiv.org/abs/2305.18053
Autor:
Boone, Zack, Palsson, Eyvindur Ari
We generalize a result of McDonald and Taylor which concerns the size of the tuples of edge lengths in the set $C_1 \times C_2$ utilizing the notion of thickness. Specifically, we show that $C_1, C_2 \subset \mathbb{R}^d$ compact sets with thickness
Externí odkaz:
http://arxiv.org/abs/2210.00675
In this paper we show that if a compact set $E \subset \mathbb{R}^d$, $d \geq 3$, has Hausdorff dimension greater than $\frac{(4k-1)}{4k}d+\frac{1}{4}$ when $3 \leq d<\frac{k(k+3)}{(k-1)}$ or $d- \frac{1}{k-1}$ when $\frac{k(k+3)}{(k-1)} \leq d$, the
Externí odkaz:
http://arxiv.org/abs/2208.07198
Autor:
Palsson, Eyvindur Ari, Sovine, Sean R.
We show that the method in recent work of Roncal, Shrivastava, and Shuin can be adapted to show that certain $L^p$-improving bounds in the interior of the boundedness region for the bilinear spherical or triangle averaging operator imply sparse bound
Externí odkaz:
http://arxiv.org/abs/2110.08928
We show for a compact set $E \subset \mathbb{R}^d$, $d \geq 4$, that if the Hausdorff dimension of $E$ is larger than $\frac{2}{3}d+1$, then the set of congruence classes of triangles formed by triples of points of $E$ has nonempty interior. Here we
Externí odkaz:
http://arxiv.org/abs/2109.13429
We establish some new $L^p$-improving bounds for the $k$-simplex averaging operators $S^k$ that hold in dimensions $d \geq k$. As a consequence of these $L^p$-improving bounds we obtain nontrivial bounds $S^k\colon L^{p_1}\times\cdots\times L^{p_k}\r
Externí odkaz:
http://arxiv.org/abs/2109.09017
We study a variant of the Erd\H os unit distance problem, concerning angles between successive triples of points chosen from a large finite point set. Specifically, given a large finite set of $n$ points $E$, and a sequence of angles $(\alpha_1,\ldot
Externí odkaz:
http://arxiv.org/abs/2104.09960
Publikováno v:
PUMP, 3, 277-307 (2020)
Motivated by the study of integer partitions, we consider partitions of integers into fractions of a particular form, namely with constant denominators and distinct odd or even numerators. When numerators are odd, the numbers of partitions for intege
Externí odkaz:
http://arxiv.org/abs/2011.14502
Integration over curved manifolds with higher codimension and, separately, discrete variants of continuous operators, have been two important, yet separate themes in harmonic analysis, discrete geometry and analytic number theory research. Here we un
Externí odkaz:
http://arxiv.org/abs/2006.09968
We find the sharp range for boundedness of the discrete bilinear spherical maximal function for dimensions $d \geq 5$. That is, we show that this operator is bounded on $l^{p}(\mathbb{Z}^d)\times l^{q}(\mathbb{Z}^d) \to l^{r}(\mathbb{Z}^d)$ for $\fra
Externí odkaz:
http://arxiv.org/abs/1911.00464