Composition-Differentiation Operator On Hardy-Hilbert Space of Dirichlet Series
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866909595400667136 |
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| author | Allu, Vasudevarao Mondal, Dipon Kumar |
| author_facet | Allu, Vasudevarao Mondal, Dipon Kumar |
| contents | In this paper, we establish a compactness criterion for the composition-differentiation operator \( D_Φ\) in terms of a decay condition of the mean counting function at the boundary of a half-plane. We provide a sufficient condition of the boundedness of the operator \( D_Φ\) for the symbol \( Φ\) with zero characteristic. Additionally, we investigate an estimate for the norm of \( D_Φ\) in the Hardy-Hilbert space of Dirichlet series, specifically with the symbol \( Φ(s) = c_1 + c_2 2^{-s} \). We also derive an estimate for the approximation numbers of the operator \( D_Φ\). Moreover, we determine an explicit conditions under which the operator \( D_Φ\) is self-adjoint and normal. Finally, we describe the spectrum of \( D_Φ\) when the symbol \( Φ(s) = c_1 + c_2 2^{-s} \). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_19939 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Composition-Differentiation Operator On Hardy-Hilbert Space of Dirichlet Series Allu, Vasudevarao Mondal, Dipon Kumar Functional Analysis Complex Variables 47B33, 47B38, 30B50, 30H10 In this paper, we establish a compactness criterion for the composition-differentiation operator \( D_Φ\) in terms of a decay condition of the mean counting function at the boundary of a half-plane. We provide a sufficient condition of the boundedness of the operator \( D_Φ\) for the symbol \( Φ\) with zero characteristic. Additionally, we investigate an estimate for the norm of \( D_Φ\) in the Hardy-Hilbert space of Dirichlet series, specifically with the symbol \( Φ(s) = c_1 + c_2 2^{-s} \). We also derive an estimate for the approximation numbers of the operator \( D_Φ\). Moreover, we determine an explicit conditions under which the operator \( D_Φ\) is self-adjoint and normal. Finally, we describe the spectrum of \( D_Φ\) when the symbol \( Φ(s) = c_1 + c_2 2^{-s} \). |
| title | Composition-Differentiation Operator On Hardy-Hilbert Space of Dirichlet Series |
| topic | Functional Analysis Complex Variables 47B33, 47B38, 30B50, 30H10 |
| url | https://arxiv.org/abs/2502.19939 |