Bounded Composition Operators on Hilbert Space of Complex-Valued Harmonic Functions
Functional Analysis
2025-03-14 v1
Abstract
In this paper, we study composition operators on Hilbert space of complex-valued harmonic functions. In particular, we explore isometries, the type of self-map that generate bounded composition operator, and characterize the boundedness of composition operator in terms of Poisson integral. Furthermore, we establish the relation between reproducing kernels and composition operators on Hilbert space of complex-valued harmonic functions.
Cite
@article{arxiv.2503.10162,
title = {Bounded Composition Operators on Hilbert Space of Complex-Valued Harmonic Functions},
author = {Tseganesh Getachew Gebrehana and Hunduma Legesse Geleta},
journal= {arXiv preprint arXiv:2503.10162},
year = {2025}
}