Fourier transforms of indicator functions, lattice point discrepancy, and the stability of integrals
Sign Up to like & getrecommendations! Published in 2018 at "Mathematische Annalen"
DOI: 10.1007/s00208-021-02156-z
Abstract: We prove sharp estimates for Fourier transforms of indicator functions of bounded open sets in $${\mathbb {R}}^n$$ R n with real analytic boundary, as well as nontrivial lattice point discrepancy results. Both are derived from… read more here.
Keywords: fourier transforms; lattice point; point discrepancy; stability ... See more keywords
Local average in hyperbolic lattice point counting, with an Appendix by Niko Laaksonen
Sign Up to like & getrecommendations! Published in 2017 at "Mathematische Zeitschrift"
DOI: 10.1007/s00209-016-1749-z
Abstract: The hyperbolic lattice point problem asks to estimate the size of the orbit $$\Gamma z$$Γz inside a hyperbolic disk of radius $$\cosh ^{-1}(X/2)$$cosh-1(X/2) for $$\Gamma $$Γ a discrete subgroup of $${\hbox {PSL}_2( {{\mathbb {R}}})} $$PSL2(R).… read more here.
Keywords: local average; hyperbolic lattice; lattice point; average hyperbolic ... See more keywords
Brunn-Minkowski type inequalities for the lattice point enumerator
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DOI: 10.1016/j.aim.2020.107193
Abstract: Geometric and functional Brunn-Minkowski type inequalities for the lattice point enumerator $\mathrm{G}_n(\cdot)$ are provided. In particular, we show that $$\mathrm{G}_n((1-\lambda)K + \lambda L + (-1,1)^n)^{1/n}\geq (1-\lambda)\mathrm{G}_n(K)^{1/n}+\lambda\mathrm{G}_n(L)^{1/n}$$ for any non-empty bounded sets $K, L\subset\mathbb{R}^n$ and all… read more here.
Keywords: brunn minkowski; type inequalities; lattice point; lambda ... See more keywords
Steinhaus' lattice-point problem for Banach spaces
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DOI: 10.1016/j.jmaa.2016.09.030
Abstract: Steinhaus proved that given a positive integer n, one may find a circle surrounding exactly n points of the integer lattice. This statement has been recently extended to Hilbert spaces by Zwolenski, who replaced the… read more here.
Keywords: steinhaus lattice; lattice point; banach spaces; point problem ... See more keywords
Nearly column-orthogonal designs based on leave-one-out good lattice point sets
Sign Up to like & getrecommendations! Published in 2017 at "Journal of Statistical Planning and Inference"
DOI: 10.1016/j.jspi.2017.01.002
Abstract: Abstract Good lattice point sets have desirable space-filling properties, and many designs with large L 1 -distance can be obtained by the leave-one-out good lattice point method (Zhou and Xu, 2015). However, there are negatively… read more here.
Keywords: good lattice; lattice point; one good; leave one ... See more keywords
Filtering spins by scattering from a lattice of point magnets
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DOI: 10.1038/s42005-020-00445-8
Abstract: Nature creates electrons with two values of the spin projection quantum number. In certain applications, it is important to filter electrons with one spin projection from the rest. Such filtering is not trivial, since spin-dependent… read more here.
Keywords: filtering spins; lattice point; physics; point ... See more keywords
Interactive Nearest Lattice Point Search in a Distributed Setting: Two Dimensions
Sign Up to like & getrecommendations! Published in 2022 at "IEEE Transactions on Communications"
DOI: 10.1109/tcomm.2022.3184170
Abstract: The nearest lattice point problem in $\mathbb {R}^{n}$ is formulated in a distributed network with $n$ nodes. The objective is to minimize the probability that an incorrect lattice point is found, subject to a constraint… read more here.
Keywords: tex math; inline formula; lattice; lattice point ... See more keywords