Aakanksha Jain

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20242026

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math.CV2026

A Canonical Positive Definite Kernel Associated with the $ξ$ -Bergman Kernel

Sahil Gehlawat, Aakanksha Jain, Amar Deep Sarkar

Let $Ω \subset C^{n}$ and $ξ \in ℓ^{1}$ . The $ξ$ -Bergman kernel $K_{ξ, Ω}$ , introduced by Bao and Guan, generalizes the classical Bergman kernel by replacing the point ev…

math.CV2025

Weighted Kernel Functions on Planar Domains

Aakanksha Jain, Kaushal Verma

We study the variation of weighted Szegő and Garabedian kernels on planar domains as a function of the weight. A Ramadanov type theorem is shown to hold as the weights vary. As a c…

math.CV2024

A Note on Kernel Functions of Dirichlet Spaces

Sahil Gehlawat, Aakanksha Jain, Amar Deep Sarkar

For a planar domain $Ω$ , we consider the Dirichlet spaces with respect to a base point $ζ \in Ω$ and the corresponding kernel functions. It is not known how these kernel functions be…

A Canonical Positive Definite Kernel Associated with the ξ-Bergman Kernel

Weighted Kernel Functions on Planar Domains

A Note on Kernel Functions of Dirichlet Spaces

A Canonical Positive Definite Kernel Associated with the $ξ$ -Bergman Kernel