In complex analysis, the Schur class is the set of holomorphic functions f {\displaystyle f} defined on the open unit disk D = { z ∈ C : | z | < 1 } {\displaystyle \mathbb {D} =\{z\in \mathbb {C} :|z|<1\}} and satisfying | f | ≤ 1 {\displaystyle |f|\leq 1} that solve the Schur problem: Given complex numbers c 0, c 1, …, c n {\displaystyle c_{0},c_{1},\dotsc,c_{n}}, find a function f = ∑ j = 0 n c j z j + ∑ j = n + 1 n f j z j {\displaystyle f=\sum _{j=0}^{n}c_{j}z^{j}+\sum _{j=n+1}^{n}f_{j}z^{j}} which is analytic and bounded by 1 on the unit disk. Wikipedia