Convexity, Markov Operators, Approximation, and Related Optimization

Octav Olteanu
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Octav Olteanu: Department of Mathematics and Informatics, University Politehnica of Bucharest, 060042 Bucharest, Romania

Mathematics, 2022, vol. 10, issue 15, 1-17

Abstract: The present review paper provides recent results on convexity and its applications to the constrained extension of linear operators, motivated by the existence of subgradients of continuous convex operators, the Markov moment problem and related Markov operators, approximation using the Krein–Milman theorem, related optimization, and polynomial approximation on unbounded subsets. In many cases, the Mazur–Orlicz theorem also leads to Markov operators as solutions. The common point of all these results is the Hahn–Banach theorem and its consequences, supplied by specific results in polynomial approximation. All these theorems or their proofs essentially involve the notion of convexity.

Keywords: convex operator; Hahn–Banach theorem; Markov moment problem; norm of the solution; Markov operator; Krein–Milman theorem; optimization; polynomial approximation; unbounded subsets; quadratic forms (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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