2009· Journal of Convex Analysis· Vol 16, pp. 605-616· 0 citations· 25 references
Abstract
We amend the theorem of A. G. Vitushkin [J. Functional Analysis 20 (1975) 149 - 157], who solves the problem of the rational approximation by constructive methods and a quasi-geometric notation – the so called analytic continuous capacity –, by a new sufficient condition. The proof is functional-analytic abstract and at the same time we can almost see the effects of the condition. We start with measures – a structure bearing level beneath the AC-capacity – and go by Cauchy transforms directly to the level of functions. Moreover we confirm a conjecture of J. Garnett [Duke Math. J. 37(1970) 689 - 699] for functions, which are continuous on the complex numbers
\mathbb{C}
C
including infinity and analytic off a Cantor-set.
The aim of this corrigendum is to reveal that in some results of our previous paper "An effective characterization of Schur-convex functions with applications" [J. Conv. Anal 14 (2007) 103-1086], and namely in Lemmas 3.1 and 3.3 and in Theorems 3.4 and 3.6, the word "measurable" should be replaced by "continuous". The...
C. Stepniak· Journal of Convex Analysis· 0 citations
In a recent paper (H. Wang, Math. Comp. 93, 2861-2884, 2024), Wang has presented a number of results concerning the convergence of approximations based on generalised Laguerre polynomials, claiming to have provided"the first rigorous proof of root-exponential convergence of Laguerre approximations for analytic function...
We prove that, for vector-valued convolution Calder\'on--Zygmund operators, boundedness on a single nontrivial Morrey space is equivalent to the corresponding global $L^p$ boundedness. Thus one Morrey scale already contains the full finite-$p$ boundedness information. The implication from Morrey to $L^p$ is obtained by...
We prove a generalization of the version, due to A. Gabrielov, of the {\L}ojasiewicz inequality for not necessarily restricted semi-Pfaffian sets. Unlike the most variants of the {\L}ojasiewicz inequality, it describes the rate of growth of a Pfaffian function on a semi-Pfaffian set $X$ not only in a neighbourhood of i...
Starting with some analysis of the support function of an arbitrary set, we obtain a formula for the subdifferential set of the supremum function of an arbitrary (possibly infinite) family of proper convex functions at each point of its effective domain, not necessarily at a continuity point. In this sense, our formula...
A. Hantoute, Marco A. López· Journal of Convex Analysis· 20 citations
In this paper, we consider a class of refined (a,b)-Fourier integral transforms defined as [Formula: see text] where a, b are nonzero arbitrary complex coefficients such that [Formula: see text]. This transform was introduced in recent work [Asian-Euro. J. Math. 15 (2022), no. 08, 2250151]. First, we establish an analo...
Tuan Trinh, Tuan Minh Nguyen, Le Van Hien et al.· Asian-European Journal of Ma...· 0 citations
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