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| Format: | Preprint |
| Veröffentlicht: |
2026
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2606.01105 |
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| _version_ | 1866916070944669696 |
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| author | Zikkos, Elias |
| author_facet | Zikkos, Elias |
| contents | Let $Λ=\{λ_n\}_{n=1}^{\infty}\subset\mathbb{N}$ with $λ_n$ strictly increasing and such that $\sum_{n=1}^{\infty}λ_n^{-1}<\infty$. We show that a Hardy subspace $H^2 (\mathbb{D}, Λ)$ consisting of functions with sparse Fourier spectrum $Λ$ coincides with a Müntz space $\overline{M^2_Λ}(\mathbb{D})$ characterized by square-summability of coefficients relative to a biorthogonal family. As consequences, we obtain a new characterization of the Hardy norm in $H^2 (\mathbb{D}, Λ)$ and an integral representation formula for the Fourier coefficients. The proof uses the biorthogonal representation developed in a previous work of the author. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2606_01105 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Hardy Subspaces with Sparse Fourier Spectrum and Muntz Space Zikkos, Elias Functional Analysis Let $Λ=\{λ_n\}_{n=1}^{\infty}\subset\mathbb{N}$ with $λ_n$ strictly increasing and such that $\sum_{n=1}^{\infty}λ_n^{-1}<\infty$. We show that a Hardy subspace $H^2 (\mathbb{D}, Λ)$ consisting of functions with sparse Fourier spectrum $Λ$ coincides with a Müntz space $\overline{M^2_Λ}(\mathbb{D})$ characterized by square-summability of coefficients relative to a biorthogonal family. As consequences, we obtain a new characterization of the Hardy norm in $H^2 (\mathbb{D}, Λ)$ and an integral representation formula for the Fourier coefficients. The proof uses the biorthogonal representation developed in a previous work of the author. |
| title | Hardy Subspaces with Sparse Fourier Spectrum and Muntz Space |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2606.01105 |