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math-ph2002★ 5 cited
Exponentials form a basis of discrete holomorphic functions
Christian Mercat
We show that discrete exponentials form a basis of discrete holomorphic functions. On a convex, the discrete polynomials form a basis as well.
math-ph2002★ 11 cited
Discrete Polynomials and Discrete Holomorphic Approximation
Christian Mercat
We use discrete holomorphic polynomials to prove that, given a refining sequence of critical maps of a Riemann surface, any holomorphic function can be approximated by a converging…
math-ph2001
Discrete period matrices and related topics
Christian Mercat
We continue our investigation of Discrete Riemann Surfaces with the discussion of the discrete analogs of period matrices, Riemann's bilinear relations, exponential of constant arg…