Gehlawat, S and Jain, A and Sarkar, AD (2025) A note on kernel functions of Dirichlet spaces. In: Journal of Mathematical Analysis and Applications, 543 (2).
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Abstract
For a planar domain Ω, we consider the Dirichlet spaces with respect to a base point ζ�Ω 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�Ω. 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. © 2024 Elsevier Inc.
| Item Type: | Journal Article |
|---|---|
| Publication: | Journal of Mathematical Analysis and Applications |
| Publisher: | Academic Press Inc. |
| Additional Information: | The copyright for this article belongs to Academic Press Inc. |
| Department/Centre: | Division of Physical & Mathematical Sciences > Mathematics |
| Date Deposited: | 19 Oct 2024 05:12 |
| Last Modified: | 19 Oct 2024 05:12 |
| URI: | http://eprints.iisc.ac.in/id/eprint/86468 |
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