English

Bergman-Szeg\H{o} asymptotic formulas and the strip problem

Complex Variables 2022-09-07 v1

Abstract

Identifying holomorphic functions by moment conditions is a classical problem. This paper explores ideas introduced by Tumanov in a well known paper on the strip problem, and building on the author's previous work, to show that weighted Bergman projections can be computed via asymptotic formulas involving Szeg\H{o} projections a fixed 1-dimensional family of curves. Various new operators are introduced; in addition, similar formulas are derived via dimension reduction, using the author's CR Hartogs theorem.

Keywords

Cite

@article{arxiv.2209.01323,
  title  = {Bergman-Szeg\H{o} asymptotic formulas and the strip problem},
  author = {Mark G. Lawrence},
  journal= {arXiv preprint arXiv:2209.01323},
  year   = {2022}
}