16 citations · 23 across the 7 of their papers we have counts for
12 papers
Another look at halfspace depth: Flag halfspaces with applications
Dušan Pokorný, Petra Laketa, Stanislav Nagy
The halfspace depth is a well studied tool of nonparametric statistics in multivariate spaces, naturally inducing a multivariate generalisation of quantiles. The halfspace depth of…
A characterization of sets in with DC distance function
Dušan Pokorný, Luděk Zajíček
We give a complete characterization of closed sets whose distance function is DC (i.e., is the difference of two convex func…
Curvatures for unions of WDC sets
Dušan Pokorný
We prove the existence of the curvature measures for a class of sets, which is a direct generalization of sets studied by Rataj and Zähle. More…
On sets in with DC distance function
Dušan Pokorný, Luděk Zajíček
We study closed sets whose distance function is DC (i.e., is the difference of two convex functions on ). Our…
On the structure of WDC sets
Dušan Pokorný, Jan Rataj, Luděk Zajíček
WDC sets in were recently defined as sublevel sets of DC functions (differences of convex functions) at weakly regular values. They form a natural and substantial g…
Kinematic formulas for sets defined by differences of convex functions
Joseph H. G. Fu, Dusan Pokorny, Jan Rataj
Two of the authors have defined the class as the class of all subsets of a smooth manifold that may be expressed in local coordinates as certain sublevel sets of DC (…
Notes on the trace problem for separately convex functions
Ondřej Kurka, Dušan Pokorný
We discuss the following question: For a function f of two or more variables which is convex in the directions of coordinate axes, how can its trace g(x) = f(x, x, ..., x) look lik…
On Removable Sets For Convex Functions
Dusan Pokorny, Martin Rmoutil
In the present article we provide a sufficient condition for a closed set F in R^d to have the following property which we call c-removability: Whenever a function f:R^d->R is loca…
Scaling exponents of curvature measures
Dusan Pokorny, Steffen Winter
Fractal curvatures of a subset F of R^d are roughly defined as suitably rescaled limits of the total curvatures of its parallel sets F_e as e tends to 0 and have been studied in th…
Nonconvex Lipschitz function in plane which is locally convex outside a discontinuum
Dusan Pokorny
We construct a Lipschitz function on $\er^{2}$ which is locally convex on the complement of some totally disconnected compact set but not convex. Existence of such function disprov…
Normal cycles and curvature measures of sets with d.c. boundary
Dusan Pokorny, Jan Rataj
We show that for every compact domain in a Euclidean space with d.c. (delta-convex) boundary there exists a unique Legendrian cycle such that the associated curvature measures fulf…
On critical values of self-similar sets
Dusan Pokorny
In the paper we study properties of the set of critical points for self-similar sets. We introduce simple condition that implies at most countably many critical values and we const…