A Note on Kernel Functions of Dirichlet Spaces
Fuente:
arXiv
Guardado en:
| Autores principales: | , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2024
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866912264027635712 |
|---|---|
| author | Gehlawat, Sahil Jain, Aakanksha Sarkar, Amar Deep |
| author_facet | Gehlawat, Sahil Jain, Aakanksha Sarkar, Amar Deep |
| contents | For a planar domain $Ω$, we consider the Dirichlet spaces with respect to a base point $ζ\inΩ$ and the corresponding kernel functions. It is not known how these kernel functions behave as we vary the base point. In this note, we prove that these kernel functions vary smoothly. As an application of the smoothness result, we prove a Ramadanov-type theorem for these kernel functions on $Ω\timesΩ$. This extends the previously known convergence results of these kernel functions. In fact, we have made these observations in a more general setting, that is, for weighted kernel functions and their higher-order counterparts. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_07457 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Note on Kernel Functions of Dirichlet Spaces Gehlawat, Sahil Jain, Aakanksha Sarkar, Amar Deep Complex Variables 30H20, 46E22 (Primary) 30C40 (Secondary) For a planar domain $Ω$, we consider the Dirichlet spaces with respect to a base point $ζ\inΩ$ and the corresponding kernel functions. It is not known how these kernel functions behave as we vary the base point. In this note, we prove that these kernel functions vary smoothly. As an application of the smoothness result, we prove a Ramadanov-type theorem for these kernel functions on $Ω\timesΩ$. This extends the previously known convergence results of these kernel functions. In fact, we have made these observations in a more general setting, that is, for weighted kernel functions and their higher-order counterparts. |
| title | A Note on Kernel Functions of Dirichlet Spaces |
| topic | Complex Variables 30H20, 46E22 (Primary) 30C40 (Secondary) |
| url | https://arxiv.org/abs/2402.07457 |