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Hardy spaces and boundary conditions from the Ising model


Functions in Hardy spaces on multiply-connected domains in the plane are given an explicit characterization in terms of a boundary condition inspired by the two-dimensional Ising model. The key underlying property is the positivity of a certain operator constructed inductively on the number of components of the boundary.

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Correspondence to Duong H. Phong.

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Hongler, C., Phong, D.H. Hardy spaces and boundary conditions from the Ising model. Math. Z. 274, 209–224 (2013).

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  • Riemann Surface
  • Line Bundle
  • Holomorphic Function
  • Unit Disk
  • Hardy Space