Applications of the Hahn-Banach Theorem, a Solution of the Moment Problem and the Related Approximation

Octav Olteanu ()
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Octav Olteanu: Independent Researcher, 061441 Bucharest, Romania

Mathematics, 2024, vol. 12, issue 18, 1-18

Abstract: We start by an application the of Krein–Milman theorem to the integral representation of completely monotonic functions. Elements of convex optimization are also mentioned. The paper continues with applications of Hahn–Banach-type theorems and polynomial approximation to obtain recent results on the moment problem on the unbounded closed interval [ 0 , + ∞ ) . Necessary and sufficient conditions for the existence and uniqueness of the solution are pointed out. Operator-valued moment problems and a scalar-valued moment problem are solved.

Keywords: geometric functional analysis; Hahn–Banach-type theorems; extreme points; simplex; moment problem; (M)-determinate measure; polynomial approximation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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