2024/10/29 by Tseganesh Getachew Gebrehana, Gebrehana, Tseganesh Getachew, Hunduma Legesse Geleta +1
Mathematics · #Acoustics #Algebraic and Geometric Analysis #Differential Equations and Boundary Problems #Harmonic #Hilbert space #Holomorphic and Operator Theory #Linguistics #Mathematical analysis #Mathematics #Mathematics education #Philosophy #Physics #Pure mathematics #Space (punctuation) #Unit (ring theory)
paper · pdf · doi:10.48550/arxiv.2410.22045
published in arXiv (Cornell University) (Cornell University)
openalex publication_date 2024/10/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.