Bergman-Szegő asymptotic formulas and the strip problem

2022/09/03 by Mark G. Lawrence, Lawrence, Mark G.
Mathematics · #30B40 #32D15 #Algebraic and Geometric Analysis #Complex Variables (math.CV) #FOS: Mathematics #Holomorphic and Operator Theory #Mathematical functions and polynomials

paper · pdf · doi:10.48550/arxiv.2209.01323

openalex publication_date 2022/09/03 · openalex created_date 2022/09/30 · openalex updated_date 2026/07/28

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 Szegő 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.

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