23 citations · 72 across the 27 of their papers we have counts for
5 papers · 1 filter
Surface dimension, tiles, and synchronising automata
Vladimir Yu. Protasov
We study the surface regularity of compact sets which is equal to the supremum of numbers such that the measure of the set doe…
The Barabanov norm is generically unique, simple, and easily computed
Vladimir Yu. Protasov
Every irreducible discrete-time linear switching system possesses an invariant convex Lyapunov function (Barabanov norm), which provides a very refined analysis of trajectories. Un…
Antinorms on cones: duality and applications
Vladimir Yu. Protasov
An antinorm is a concave nonnegative homogeneous functional on a convex cone. It is shown that if the cone is polyhedral, then every antinorm has a unique continuous extension from…
Tiling of polyhedral sets
Vladimir Yu. Protasov, Tatyana Zaitseva
A self-affine tiling of a compact set G of positive Lebesgue measure is its partition to parallel shifts of a compact set which is affinely similar to G. We find all polyhedral set…
On mutually inverse transforms of functions on a half-line
V. Yu. Protasov, M. E. Shirokov
Two transforms of functions on a half-line are considered. It is proved that their composition gives a concave majorant for every nonnegative function. In particular, this composit…