Interpolation, Prekopa and Brunn-Minkowski for $F$-subharmonicity
Julius Ross, David Witt Nystr\"om
TL;DR
This paper generalizes classical convexity theorems to $F$-subharmonic functions, introducing a new harmonic interpolation concept that broadens the scope of Minkowski addition and convex set interpolation.
Contribution
It extends Prekopa's and Brunn-Minkowski's theorems to $F$-subharmonicity and introduces harmonic interpolation as a novel generalization of Minkowski addition.
Findings
Extended classical theorems to $F$-subharmonic functions
Introduced harmonic interpolation for convex functions and sets
Provided a new framework for interpolation in convex analysis
Abstract
We extend Prekopa's Theorem and the Brunn-Minkowski Theorem from convexity to -subharmonicity. We apply this to the interpolation problem of convex functions and convex sets introducing a new notion of "harmonic interpolation" that we view as a generalization of Minkowski-addition.
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Taxonomy
TopicsPoint processes and geometric inequalities · Advanced Banach Space Theory · Holomorphic and Operator Theory