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| Format: | Preprint |
| Veröffentlicht: |
2026
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2601.02217 |
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| _version_ | 1866908748379848704 |
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| author | Fricain, Emmanuel Mashreghi, Javad |
| author_facet | Fricain, Emmanuel Mashreghi, Javad |
| contents | We present an explicit formula for the orthogonal projection onto the subspace of analytic polynomials of degree at most $n$ in the local Dirichlet space $D_μ$ , where the positive measure $μ$ consists of a finite number of Dirac measures located at points on the unit circle $\mathbb T$. This result has two key aspects: first, while it is known that polynomials are dense in $D_μ$ , this approach offers a concrete linear approximation scheme within the space. Second, due to the orthogonality of the polynomials involved, the scheme is qualitative, as the distance of an arbitrary function $f\in D_μ$ to the projected subspace is explicitly determined. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_02217 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Orthogonal projections in the local Dirichlet spaces Fricain, Emmanuel Mashreghi, Javad Complex Variables We present an explicit formula for the orthogonal projection onto the subspace of analytic polynomials of degree at most $n$ in the local Dirichlet space $D_μ$ , where the positive measure $μ$ consists of a finite number of Dirac measures located at points on the unit circle $\mathbb T$. This result has two key aspects: first, while it is known that polynomials are dense in $D_μ$ , this approach offers a concrete linear approximation scheme within the space. Second, due to the orthogonality of the polynomials involved, the scheme is qualitative, as the distance of an arbitrary function $f\in D_μ$ to the projected subspace is explicitly determined. |
| title | Orthogonal projections in the local Dirichlet spaces |
| topic | Complex Variables |
| url | https://arxiv.org/abs/2601.02217 |