Algebraic genericity of frequently universal harmonic functions on trees
N. Biehler, V. Nestoridis, A. Stavrianidi
TL;DR
This paper demonstrates that the set of frequently universal harmonic functions on a tree forms a dense vector space within all harmonic functions, extending the theory to harmonic functions valued in any separable Fréchet space.
Contribution
It introduces a generalized framework for universal harmonic functions on trees, replacing the complex plane with any separable Fréchet space, and proves the density of such functions.
Findings
The set of frequently universal harmonic functions contains a dense vector space.
The theory is extended from complex-valued to E-valued harmonic functions for any separable Fréchet space.
Universal harmonic functions are shown to be abundant in the space of all harmonic functions.
Abstract
We show that the set of frequently universal harmonic functions on a tree T contains a vector space except 0 which is dense in the space of harmonic functions on T seen as subset of C^T . In order to prove this we replace the complex plane C by any separable Frechet space E and we repeat all the theory.
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Taxonomy
TopicsHolomorphic and Operator Theory · Geometry and complex manifolds · Mathematical Analysis and Transform Methods