Add to ORKGAbstract. Given a positive integer n, one may find a circle on the Euclidean plane surrounding exactly n points of the integer lattice. This classical geometric fact due to Steinhaus has been recently extended to Hilbert spaces by Zwoleński, who replaced the integer lattice by any infinite set which intersects every ball in at most finitely many points. We investigate the Banach spaces satisfying this property, which we call (S), and show that all strictly convex Banach spaces have (S). Nonetheless, we construct a norm in dimension three which has (S) but fails to be strictly convex. 1
We prove a fairly general inequality that estimates the number of latticepoints in a ball of positiv...
It has been shown that the three-circles theorem, which is also known as Titeica's or Johnson's theo...
We prove that, given any covering of any infinite-dimensional Hilbert space $H$ by countably many cl...
Steinhaus proved that given a positive integer n, one may find a circle surrounding exactly n points...
Steinhaus proved that given a positive integer n, one may find a circle surrounding exactly n points...
AbstractIt is proved that for any integern≥0, there is a circle in the plane that passes through exa...
A planar set is said to have the Steinhaus property if however it is placed on $R2$, it contains exa...
We investigate various problems related to convexity in the three spaces of constant curvature (the ...
A planar set is said to have the Steinhaus property if however it is placed on $R2$, it contains exa...
We prove that every separable polyhedral Banach space X is isomorphic to a polyhedral Banach space Y...
When a strictly convex plane set S moves by translation, the set J of points of the integer lattice ...
When a strictly convex plane set S moves by translation, the set J of points of the integer lattice ...
Dedicated to the memory of Tom Wolff We give a short proof of the fact that there are no measurable ...
A uniformly distributed discrete set of points in the plane called lattices are considered. The most...
The following is known as the geometric hypothesis of Banach: let V be an m-dimensional Banach spa...
We prove a fairly general inequality that estimates the number of latticepoints in a ball of positiv...
It has been shown that the three-circles theorem, which is also known as Titeica's or Johnson's theo...
We prove that, given any covering of any infinite-dimensional Hilbert space $H$ by countably many cl...
Steinhaus proved that given a positive integer n, one may find a circle surrounding exactly n points...
Steinhaus proved that given a positive integer n, one may find a circle surrounding exactly n points...
AbstractIt is proved that for any integern≥0, there is a circle in the plane that passes through exa...
A planar set is said to have the Steinhaus property if however it is placed on $R2$, it contains exa...
We investigate various problems related to convexity in the three spaces of constant curvature (the ...
A planar set is said to have the Steinhaus property if however it is placed on $R2$, it contains exa...
We prove that every separable polyhedral Banach space X is isomorphic to a polyhedral Banach space Y...
When a strictly convex plane set S moves by translation, the set J of points of the integer lattice ...
When a strictly convex plane set S moves by translation, the set J of points of the integer lattice ...
Dedicated to the memory of Tom Wolff We give a short proof of the fact that there are no measurable ...
A uniformly distributed discrete set of points in the plane called lattices are considered. The most...
The following is known as the geometric hypothesis of Banach: let V be an m-dimensional Banach spa...
We prove a fairly general inequality that estimates the number of latticepoints in a ball of positiv...
It has been shown that the three-circles theorem, which is also known as Titeica's or Johnson's theo...
We prove that, given any covering of any infinite-dimensional Hilbert space $H$ by countably many cl...