19 citations · 27 across the 17 of their papers we have counts for
17 papers
Remote temperature sensing in 2D and the Bergman kernel
Steven R. Bell, Leah McNabb
We explore the problem of estimating the steady state temperature in a two-dimensional domain at a point knowing the temperature to high order at another point. We find connections…
A new way to express boundary values in terms of holomorphic functions on planar Lipschitz domains
Steven R. Bell, Loredana Lanzani, Nathan A. Wagner
We decompose - integrable functions on the boundary of a simply connected Lipschitz domain into the sum of the boundary values of two, uniquely determined…
Real algebraic geometry of real algebraic Jordan curves in the plane and the Bergman kernel
Steven R. Bell
We characterize the space of restrictions of real rational functions to certain algebraic Jordan curves in the plane via the Dirichlet-to-Neumann map associated to the domain in th…
Something about Poisson and Dirichlet
Steven R. Bell, Luis Reyna de la Torre
We solve the Dirichlet problem in the unit disc and derive the Poisson formula using very elementary methods and explore consequent simplifications in other foundational areas of c…
Ruminations on Hejhal's theorem about the Bergman and Szego kernels
Steven R. Bell, Bjorn Gustafsson
We give a new proof of Dennis Hejhal's theorem on the nondegeneracy of the matrix that appears in the identity relating the Bergman and Szego kernels of a smoothly bounded finitely…
The Dirichlet and Neumann and Dirichlet-to-Neumann problems in quadrature, double quadrature, and non-quadrature domains
Steven R. Bell
We demonstrate that solving the classical problems mentioned in the title on quadrature domains when the given boundary data is rational is as simple as the method of partial fract…