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arXiv · 2305.16920

Boundary integral representation of multipliers of fragmented affine functions and other intermediate function spaces

Ondřej F. K. Kalenda·Jakub Rondoš·Jiří Spurný
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Abstract

We develop a theory of abstract intermediate function spaces on a compact convex set $X$ and study the behaviour of multipliers and centers of these spaces. In particular, we provide some criteria for coincidence of the center with the space of multipliers and a general theorem on boundary integral representation of multipliers. We apply the general theory in several concrete cases, among others to strongly affine Baire functions, to the space $A_f(X)$ of fragmented affine functions, to the space $(A_f(X))^\mu$, the monotone sequential closure of $A_f(X)$, to their natural subspaces formed by Borel functions, or, in some special cases, to the space of all strongly affine functions. In addition, we prove that the space $(A_f(X))^\mu$ is determined by extreme points and provide a large number of illustrating examples and counterexamples.

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Ondřej F. K. Kalenda, Jakub Rondoš, Jiří Spurný. 2023-05-26. Boundary integral representation of multipliers of fragmented affine functions and other intermediate function spaces. https://doi.org/10.1007/s12215-025-01249-x

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