O křivkách maximální délky
On a class of variational integrals over BV varieties
We present here our most recent results ([1def]) about the definition of non-linear Weiertrass-type integrals over BV varieties, possibly discontinuous and not necessarily Sobolev's.
On a generalisation of the Hahn-Jordan decomposition for real càdlàg functions
For a real càdlàg function f and a positive constant c we find another càdlàg function which has the smallest total variation among all functions uniformly approximating f with accuracy c/2. The solution is expressed in terms of truncated variation, upward truncated variation and downward truncated variation introduced in earlier work of the author. They are always finite even if the total variation of f is infinite, and they may be viewed as a generalisation of the Hahn-Jordan decomposition for...
On absolutely kth continuous functions
On characterization of the Lipschitzian composition operator between spaces of functions of bounded -variation
On differentiability of Peano type functions
On differentiability of Peano type functions
On differentiability of Peano type functions. II
On embedding of the class .
On essential -variation.
On functions of bounded n-th variation
On functions of bounded (p,2)-variation.
On generalized variations (II)
On Kurzweil-Stieltjes equiintegrability and generalized BV functions
We present sufficient conditions ensuring Kurzweil-Stieltjes equiintegrability in the case when integrators belong to the class of functions of generalized bounded variation.
On Some Properties of Functions of Generalized Variation.
On the Absolute Continuity of a Surface Representation
On the absolute convergence of small gaps Fourier series of functions of .
On the embedding Waterman, Chanturia and generalized Wiener classes in the classes .
On the extension and generation of set-valued mappings of bounded variation
We study set-valued mappings of bounded variation of one real variable. First we prove the existence of an extension of a metric space valued mapping from a subset of the reals to the whole set of reals with preservation of properties of the initial mapping: total variation, Lipschitz constant or absolute continuity. Then we show that a set-valued mapping of bounded variation defined on an arbitrary subset of the reals admits a regular selection of bounded variation. We introduce a notion of generated...
On the failure of a decomposition