Hilbert Space of Complex-Valued Harmonic Functions in the Unit Disc
Complex Variables
2024-10-30 v1
Abstract
We investigate an extended version of Hilbert space of analytic functions called Hilbert space of complex-valued harmonic functions. It is found that functions in Hilbert space of complex-valued harmonic functions exhibit many properties analogous to its analytic counter part such as complex-valued harmonic function analogous of norm, equivalent norms, reproducing kernels, growth estimates and Littlewood-Paley Identity Theorem. In conclusion we prove that many results in Hilbert space of analytic functions also hold in larger Hilbert space of complex-valued harmonic functions.
Cite
@article{arxiv.2410.22045,
title = {Hilbert Space of Complex-Valued Harmonic Functions in the Unit Disc},
author = {Tseganesh Getachew Gebrehana and Hunduma Legesse Geleta},
journal= {arXiv preprint arXiv:2410.22045},
year = {2024}
}