  The name Schur is associated with many terms and concepts that are widely
used in a number of diverse fields of mathematics and engineering. This survey
article focuses on Schur's work in analysis. Here too, Schur's name is
commonplace: The Schur test and Schur-Hadamard multipliers (in the study of
estimates for Hermitian forms), Schur convexity, Schur complements, Schur's
results in summation theory for sequences (in particular, the fundamental
Kojima-Schur theorem), the Schur-Cohn test, the Schur algorithm, Schur
parameters and the Schur interpolation problem for functions that are
holomorphic and bounded by one in the unit disk. In this survey, we discuss all
of the above mentioned topics and then some, as well as some of the
generalizations that they inspired. There are nine sections of text, each of
which is devoted to a separate theme based on Schur's work. Each of these
sections has an independent bibliography. There is very little overlap. A tenth
section presents a list of the papers of Schur that focus on topics that are
commonly considered to be analysis. We begin with a review of Schur's less
familiar papers on the theory of commuting differential operators.
