We first review both the theory of discrete analytic functions and the main features of Schur analysis (a collection of problems pertaining to functions analytic and contractive in the open unit disk, and with a wide range of applications). Then, we present new connections between the theory of discrete analytic functions and Schur analysis. This allows us to define a new class of problems pertaining to discrete analytic functions.
D. Alpay, P. Jorgensen, R. Seager, and D. Volok. On discrete analytic functions: Products, Rational Functions, and Reproducing Kernels. Journal of Applied Mathematics and Computing. Volume 41, Issue 1 (2013), Page 393-426.
D. Alpay and D. Volok, Discrete analytic functions and Schur analysis. Preprint, 2021.