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Joel Shapiro (mathematician)
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.
==Career==
Shapiro completed his PhD thesis entitled "Linear Functionals on Non-Locally Convex Spaces" under the supervision of Allen Shields in 1969 at the University of Michigan.〔Math Genealogy, http://genealogy.math.ndsu.nodak.edu/id.php?id=5423〕 Upon Graduating, he became a Research Associate at Queen's University, Canada, then from 1970 onwards climbed the ranks at Michigan State University, becoming a full Professor in 1979. He stayed at Michigan until 2006, when he retired and became and Adjunct Professor at Portland State University in Oregon.
Shapiro discovered some of the most important properties of composition operators, including a study of the cyclic properties of such operators〔P. S. Bourdon and J. H. Shapiro, Mem. Amer. Math. Soc. 125 (1997), no. 596, pp. 1-105〕 and the first calculations of the essential norm 〔J. H. Shapiro, The essential norm of a composition operator. Ann. of Math. (2) 125 (1987), no. 2, 375–404.〕 for composition operators on the Hardy spaces of the Unit disc.
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