Hilbert Space of Complex-Valued Harmonic Functions in the Unit Disc
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866929566872764416 |
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| author | Gebrehana, Tseganesh Getachew Geleta, Hunduma Legesse |
| author_facet | Gebrehana, Tseganesh Getachew Geleta, Hunduma Legesse |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_22045 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Hilbert Space of Complex-Valued Harmonic Functions in the Unit Disc Gebrehana, Tseganesh Getachew Geleta, Hunduma Legesse Complex Variables 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. |
| title | Hilbert Space of Complex-Valued Harmonic Functions in the Unit Disc |
| topic | Complex Variables |
| url | https://arxiv.org/abs/2410.22045 |