Name
Abstract | ||
|---|---|---|
Given any positive integers m and d, we say a sequence of points (x(i))(i is an element of I) in R-m is Lipschitz-d-controlling if one can select suitable values y(i)(i is an element of I) such that for every Lipschitz function f : R-m -> R-d there exists i with vertical bar f (x(i)) - Y-i vertical bar < 1. We conjecture that for every m <= d, a sequence (x(i))(i is an element of I )subset of R-m is d-controlling if and only if sup(n is an element of N)vertical bar{i is an element of I : vertical bar X-i vertical bar <= n}vertical bar/n(d) = infinity. We prove that this condition is necessary and a slightly stronger one is already sufficient for the sequence to be d-controlling. We also prove the conjecture for m = 1. |
Year | DOI | Venue |
|---|---|---|
2017 | 10.1112/S0025579318000311 | MATHEMATIKA |
DocType | Volume | Issue |
Journal | 64 | 3 |
ISSN | Citations | PageRank |
0025-5793 | 0 | 0.34 |
References | Authors | |
0 | 3 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Andrey B. Kupavskii | 1 | 64 | 22.31 |
| János Pach | 2 | 2366 | 292.28 |
| Gábor Tardos | 3 | 1261 | 140.58 |