4 papers
On the Existence of Solutions to the Seiberg-Witten Vortex Equations with Exponential Decay on the Plane
William L. Blair, Minh Lam Nguyen
Clifford Taubes showed that the moduli space of the variational equations of the Yang-Mills-Higgs functional on the plane is non-empty, and its elements correspond to "vortices". I…
Bicomplex Hardy Classes of Solutions to Beltrami Equations and the Schwarz Boundary Value Problem
William L. Blair
We define Hardy classes of bicomplex-valued functions on the complex unit disk which solve bicomplex versions of the Beltrami and related equations. Using representations in terms…
An Atomic Representation for Bicomplex Hardy Classes
William L. Blair
We develop representations for bicomplex-valued functions in Hardy classes that generalize the complex holomorphic Hardy spaces. Using these representations, we show these function…
Bicomplex Schwarz and Dirichlet Boundary Value Problems
William L. Blair
We define and solve boundary value problems of Schwarz and Dirichlet type on the complex unit disk for bicomplex-valued functions.