3 papers
math.CV2026
A Canonical Positive Definite Kernel Associated with the -Bergman Kernel
Sahil Gehlawat, Aakanksha Jain, Amar Deep Sarkar
Let and . The -Bergman kernel , 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 , we consider the Dirichlet spaces with respect to a base point and the corresponding kernel functions. It is not known how these kernel functions be…