Mark G. Lawrence

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20142025

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math.CV2022

Real Analytic Bergman Spaces

Mark G. Lawrence

The usual examples of Bergman spaces consist of the closure of an algebra of holomorphic functions on a domain. One can also take the real part of such functions, but essentially o…

math.CV2022

Bergman-Szegő asymptotic formulas and the strip problem

Mark G. Lawrence

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 build…

math.CV2018

Polynomial hull of a torus fibered over the circle

Julien Duval, Mark Lawrence

Given a 2-sheeted torus over the circle with winding number 1, we prove that its polynomial hull is a union of 2-sheeted holomorphic discs. Moreover when the hull is non degenerate…

math.CV2015

The $L^{p}$ CR Hartogs separate analyticity theorem for strictly convex domains

Mark G. Lawrence

For a large class of convex domains in $C^{n}$ , it is shown that an $L^{p}$ function on the boundary is CR if there are holomorphic extensions on almost all slices of D by complex…

math.CV2014

Bernstein-Walsh inequalities in higher dimensions over exponential curves

Shirali Kadyrov, Mark Lawrence

Let $x = (x_{1}, \dots, x_{d}) \in [- 1, 1]^{d}$ be linearly independent over $Z$ , set $K = {(e^{z}, e^{x_{1} z}, e^{x_{2} z} \dots, e^{x_{d} z}) : ∣ z ∣ \leq 1} .$ We prove sharp estimates for…

Real Analytic Bergman Spaces

Bergman-Szegő asymptotic formulas and the strip problem

Polynomial hull of a torus fibered over the circle

The Lp CR Hartogs separate analyticity theorem for strictly convex domains

Bernstein-Walsh inequalities in higher dimensions over exponential curves

The $L^{p}$ CR Hartogs separate analyticity theorem for strictly convex domains