The reduced Bergman kernel and its properties-Reference-Cited by-同舟云学术

The reduced Bergman kernel and its properties

Published:2023-03 Issue:03 Volume:34 Page:
ISSN:0129-167X
Container-title:International Journal of Mathematics
language:en
Short-container-title:Int. J. Math.

Author:

Gehlawat Sahil¹^ORCID,Jain Aakanksha²,Sarkar Amar Deep³

Affiliation:

1. Harish-Chandra Research Institute, A CI of Homi Bhabha National Institute, Chhatnag Road, Jhunsi, Prayagraj - 211019, India

2. Department of Mathematics, Indian Institute of Science, Bangalore 560 012, India

3. Indian Institute of Science Education and Research Kolkata, India

Abstract

In this paper, we study some properties of the nth-order weighted reduced Bergman kernels for planar domains, [Formula: see text]. Specifically, we look at Ramadanov type theorems, localization, and boundary behavior of the weighted reduced Bergman kernel and its higher-order counterparts. We also give a transformation formula for these kernels under biholomorphisms.

Funder

Harish-Chandra Research Institute

PMRF : Prime Minister Research Fellowship INDIA

Indian Institute of Science Education and Research Kolkata

Publisher

World Scientific Pub Co Pte Ltd

Subject

General Mathematics

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0129167X23500155

Reference13 articles.

1. S. Bergman , The Kernel Function and Conformal Mapping, 2nd Revised edn. Mathematical Surveys, Vol. 5 (American Mathematical Society, Providence, R.I., 1970), x+257 pp.

2. The higher order curvatures of weighted span metrics on Riemann surfaces

3. Transformation Formula for the Reduced Bergman Kernel and its Application

4. R. E. Greene, K.T. Kim and S. G. Krantz , The Geometry of Complex Domains, Progress in Mathematics, Vol. 291 (Birkhuser Boston, Ltd., Boston, MA, 2011), xiv+303 pp.

5. L2 estimates and existence theorems for the $\bar \partial $ operator