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Regular version of the site
Of all publications in the section: 8
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Article
Safronenko E. Studia Mathematica. 2021. Vol. 259. P. 153-173.

This paper is devoted to measures of symmetry based on the distance from the centroid to one of the centers of the John and the Löwner ellipsoid. The accuracy of the derived upper bounds for the relevant measures of symmetry is proven.

Added: Apr 17, 2021
Article
Baranov A., Belov Y., Borichev А. Studia Mathematica. 2017. Vol. 236. P. 127-142.

We describe the radial Fock type spaces which have Riesz bases of normalized reproducing kernels and which are (or are not) isomorphic to de Branges spaces in terms of weight functions.

Added: Jun 7, 2017
Article
Pirkovskii A. Y. Studia Mathematica. 1999. Vol. 133. No. 2. P. 163-174.
Added: Oct 7, 2010
Article
V.V.Chistyakov, Rychlewicz A. Studia Mathematica. 2002. Vol. 153. No. 3. P. 235-247.

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 de ned on an arbitrary subset of the reals admits a regular selection of bounded variation. We introduce a notion of generated setvalued mappings and show that, under suitable assumptions, set-valued mappings (with arbitrary domains) which are Lipschitzian, of bounded variation or absolutely continuous are generated by certain families of mappings with nice properties. Finally, we prove a Castaing type representation theorem for set-valued mappings of bounded variation.

Added: Nov 10, 2009
Article
Vladimir Lebedev. Studia Mathematica. 2019. Vol. 247. No. 3. P. 273-283.

We consider the Wiener algebra A(T^d) of absolutely convergent Fourier series on the d-torus. For phase functions \phi of a certain special form we obtain lower bounds for the A -norms of e^{i\lambda\varphi} as \lambda tends to \infty.

Added: Mar 23, 2018
Article
Vladimir Lebedev. Studia Mathematica. 2015. Vol. 231. No. 1. P. 73-81.

The well-known Bohr--Pal theorem asserts that for every continuous real-valued function f on the circle T there exists a change of variable, i.e., a homeomorphism h of T onto itself, such that the Fourier series of the superposition foh converges uniformly. Subsequent improvements of this result imply that actually there exists a homeomorphism that brings f into the Sobolev space W_2^{1/2}(T). This refined version of the Bohr--Pal theorem does not extend to complex-valued functions. We show that if \alpha<1/2, then there exists a complex-valued f that satisfies the Lipschitz condition of order \alpha and at the same time has the property that foh is not in W_2^{1/2}(T) for every homeomorphism h of T.

Added: Feb 16, 2016
Article
Vyacheslav V. Chistyakov, Svetlana A. Chistyakova. Studia Mathematica. 2017. Vol. 238. No. 1. P. 37-57.

Given a subset $T$ of the reals $R$ and a metric space $M$, we introduce a nondecreasing sequence $\{\nu_n\}$ of pseudometrics on $M^T$ (the set of all functions from $T$ into $M$), called the joint modulus of variation. We prove that if two sequences $\{f_j\}$ and $\{g_j\}$ of functions from $M^T$ are such that $\{f_j\}$ is pointwise precompact, $\{g_j\}$ is pointwise convergent, and the limit superior of $\nu_n(f_j,g_j)$ as $j\to\infty$ is $o(n)$ as $n\to\infty$, then $\{f_j\}$ admits a pointwise convergent subsequence whose limit is a conditionally regulated function. We illustrate the sharpness of this result by examples (in particular, the assumption on the lim sup is necessary for uniformly convergent sequences $\{f_j\}$ and $\{g_j\}$, and `almost necessary' when they converge pointwise) and show that most of the known Helly-type pointwise selection theorems are its particular cases.

Added: May 11, 2017
Article
Vladimir Lebedev. Studia Mathematica. 2014. Vol. 220. No. 3. P. 265-276.

We consider sets in the real line that have Littlewood properties LP(p) or LP and study the following question: How thick can these sets be?

Added: Apr 18, 2014