Bergman-Szeg\H{o} asymptotic formulas and the strip problem
Mark G. Lawrence
TL;DR
This paper develops asymptotic formulas connecting Bergman and Szeg\
Contribution
It introduces new operators and formulas that relate weighted Bergman projections to Szeg\
Findings
Asymptotic formulas link Bergman and Szeg\
New operators are introduced for the analysis
Formulas derived via dimension reduction using CR Hartogs theorem
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.
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Taxonomy
TopicsHolomorphic and Operator Theory · Algebraic and Geometric Analysis · Mathematical functions and polynomials