2023/08/14 by Aakanksha Jain, Jain, Aakanksha, Kaushal Verma +1 · 1 citation
Mathematics · #2020. Primary: 30C40 #Analytic and geometric function theory #Complex Variables (math.CV) #FOS: Mathematics #Geometry and complex manifolds #Holomorphic and Operator Theory #Secondary: 31A99
paper · pdf · doi:10.48550/arxiv.2308.07021
openalex publication_date 2023/08/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study properties of weighted Szegő and Garabedian kernels on planar domains. Motivated by the unweighted case as explained in Bell's work, the starting point is a weighted Kerzman-Stein formula that yields boundary smoothness of the weighted Szegő kernel. This provides information on the dependence of the weighted Szegő kernel as a function of the weight. When the weights are close to the constant function 1 (which corresponds to the unweighted case), it is shown that some properties of the unweighted Szegő kernel propagate to the weighted Szegő kernel as well. Finally, it is shown that the reduced Bergman kernel and higher order reduced Bergman kernels can be written as a rational combination of three unweighted Szegő kernels and their conjugates, thereby extending Bell's list of kernel functions that are made up of simpler building blocks that involve the Szegő kernel.