Hahn-Banach Theorem, Polynomial Approximation, Moment Problems, and Related Inverse Problems
A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Engineering Mathematics".
Deadline for manuscript submissions: closed (31 July 2021) | Viewed by 5890
Special Issue Editor
Interests: Hahn-Banach-type theorems; Markov moment problems; polynomial approximation on special unbounded subsets; charaterization of isotonicity of convex operators defined on a convex cone
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Special Issue Information
Dear Colleagues,
As is well-known, Hahn-Banach-type results have their main applications in solving moment problems, the subdifferentiability of convex operators, controlled regularity, and characterizing the isotonicity of convex operators defined on a convex cone in terms of their subdifferentials. Such problems represent motivations of finding necessary and sufficient conditions for the existence of a linear extension from a vector subspace to the entire domain space, which is dominated by a convex operator and dominates a concave operator. These convex (and, respectively, concave) operators are defined on arbitrary convex subsets. For applications, topological versions of such results are emphasized. In this respect, the continuous convex-dominating operator usually controls the norm of the linear extension. Polynomial approximation on Cartesian products of unbounded closed intervals has been also applied to characterize the existence and uniqueness of the solution for some Markov moment problems in terms of quadratic forms. One partially solves the difficulty arising from the fact that, in several dimensions, there exist nonnegative polynomials that are not sums of squares. We invite the authors of related papers to submit them for publication in this Special Issue.
Prof. Dr. Octav Olteanu
Guest Editor
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Keywords
- Hahn-Banach theorem
- Markov moment problems
- Markov operators
- polynomial approximation
- quadratic forms
- isotone convex operators over a convex cone
