Joel H. Shapiro is a US mathematician, and one of the leading experts in the field of composition operators. He is the author of the book "Composition Operators and Classical Function Theory" (ISBN 3540940677), and the American Mathematical Society memoir "Cyclic Phenomena for Composition Operators" (Memoirs of the American Math. Society #596, Vol. 125, 1997, pp. 1–105), with Paul Bourdon.