Zobrazeno 1 - 10
of 76
pro vyhledávání: '"Zajicek, Ludek"'
Autor:
Johanis, Michal, Zajíček, Luděk
Our note is a complement to recent articles \cite{JS1} (2011) and \cite{JS2} (2013) by M. Jim\'enez-Sevilla and L. S\'anchez-Gonz\'alez which generalise (the basic statement of) the classical Whitney extension theorem for $C^1$-smooth real functions
Externí odkaz:
http://arxiv.org/abs/2403.14317
Our paper is a complement to a recent article by D. Azagra and C. Mudarra (2021). We show how older results on semiconvex functions with modulus $\omega$ easily imply extension theorems for $C^{1,\omega}$-smooth functions on super-reflexive Banach sp
Externí odkaz:
http://arxiv.org/abs/2305.19995
Autor:
Zajicek, Ludek
Let $X_1, \dots, X_n$ be Banach spaces and $f$ a real function on $X=X_1 \times\dots \times X_n$. Let $A_f$ be the set of all points $x \in X$ at which $f$ is partially Fr\' echet differentiable but is not Fr\' echet differentiable. Our results imply
Externí odkaz:
http://arxiv.org/abs/2209.12679
Autor:
Zajicek, Ludek
Answering a question asked by K.C. Ciesielski and T. Glatzer in 2013, we construct a $C^1$-smooth function $f$ on $[0,1]$ and a set $M \subset \operatorname{graph} f$ nowhere dense in $\operatorname{graph} f$ such that there does not exist any linear
Externí odkaz:
http://arxiv.org/abs/2201.00772
Autor:
Kossaczka, Marta, Zajicek, Ludek
Sanchez, Viader, Paradis and Carrillo (2016) proved that there exists an increasing continuous singular function $f$ on $[0,1]$ such that the set $A_f$ of points where $f$ has a nonzero finite derivative has Hausdorff dimension 1 in each subinterval
Externí odkaz:
http://arxiv.org/abs/2111.14519
Publikováno v:
In Journal of Mathematical Analysis and Applications 1 April 2024 532(1)
Autor:
Kryštof, Václav, Zajíček, Luděk
Let $G \subset {\mathbb R}^{n}$ be an open convex set which is either bounded or contains a translation of a convex cone with nonempty interior. It is known that then, for every modulus $\omega$, every function on $G$ which is both semiconvex and sem
Externí odkaz:
http://arxiv.org/abs/2103.00524
Autor:
Pokorný, Dušan, Zajíček, Luděk
We give a complete characterization of closed sets $F \subset \mathbb{R}^2$ whose distance function $d_F:= \mathrm{dist}(\cdot,F)$ is DC (i.e., is the difference of two convex functions on $\mathbb{R}^2$). Using this characterization, a number of pro
Externí odkaz:
http://arxiv.org/abs/2006.04303
Autor:
Pokorný, Dušan, Zajíček, Luděk
We study WDC sets, which form a substantial generalization of sets with positive reach and still admit the definition of curvature measures. Main results concern WDC sets $A\subset \mathbb{R}^2$. We prove that, for such $A$, the distance function $d_
Externí odkaz:
http://arxiv.org/abs/1905.12709
Autor:
Pokorný, Dušan, Zajíček, Luděk
We study closed sets $F \subset {\mathbb R}^d$ whose distance function $d_F:= {\rm dist}\,(\cdot,F)$ is DC (i.e., is the difference of two convex functions on ${\mathbb R}^d$). Our main result asserts that if $F \subset {\mathbb R}^2$ is a graph of a
Externí odkaz:
http://arxiv.org/abs/1904.12223