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The "Golden" Number Theory and New Properties of Natural Numbers
The main purpose of the present article is to give a brief description of the “golden” number theory and new properties of natural numbers following from it, in pa rticular, Z-property, D-property, Φ…
From the Hahn–Banach extension theorem to the isotonicity of convex functions and the majorization theory
The property of isotonicity of a continuous convex function on the positive cone is characterized via subdifferentials. This is used to illustrate a new generalization of the Hardy–Littlewood–Polya…
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Polynomial Approximation on Unbounded Subsets, Markov Moment Problem and Other Applications
This paper starts by recalling the author’s results on polynomial approximation over a Cartesian product A of closed unbounded intervals and its applications to solving Markov moment problems. Under…
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On Markov Moment Problem and Related Results
TLDR
New results and theorems on the vector-valued Markov moment problem are proved by means of polynomial approximation on unbounded subsets, also applying an extension of the positive linear operators’ result.
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On truncated and full classical Markov moment problems
Abstract Giving necessary and sufficient conditions for the existence of solutions of truncated and full classical Markov moment problems in terms of the given (or measured) moments, in Lp,μ (S) (1 ≤…
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From Hahn–Banach Type Theorems to the Markov Moment Problem, Sandwich Theorems and Further Applications
The aim of this review paper is to recall known solutions for two Markov moment problems, which can be formulated as Hahn–Banach extension theorems, in order to emphasize their relationship with the…
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New Results on Markov Moment Problem
The present work deals with the existence of the solutions of some Markov moment problems. Necessary conditions, as well as necessary and sufficient conditions, are discussed. One recalls the…
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On Hahn-Banach theorem and some of its applications
Abstract First, this work provides an overview of some of the Hahn-Banach type theorems. Of note, some of these extension results for linear operators found recent applications to isotonicity of…
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Approximation and Markov moment problem on concrete spaces
Polynomial approximation results on unbounded subsets of $$R^n$$Rn are discussed. By applying these results, one obtains characterizations of the existence of the solutions of the multidimensional…
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EXTENSION AND DECOMPOSITION OF LINEAR OPERATORS DOMINATED BY CONTINUOUS INCREASING SUBLINEAR OPERATORS
moment problem are stated in [10]. Further applications to the classical moment problem are proved in [6], [11] – [15]. The article [13] contains a polynomial approximation result valid on unbounded…
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