Joel Shapiro (mathematician)
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Joel H. Shapiro is an American
mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...
, active in the field of
composition operator In mathematics, the composition operator C_\phi with symbol \phi is a linear operator defined by the rule C_\phi (f) = f \circ \phi where f \circ \phi denotes function composition. It is also encountered in composition of permutations in permutati ...
s. He is the author of the book ''Composition Operators and Classical Function Theory'' (), and the
American Mathematical Society The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, ...
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 A Doctor of Philosophy (PhD, DPhil; or ) is a terminal degree that usually denotes the highest level of academic achievement in a given discipline and is awarded following a course of graduate study and original research. The name of the deg ...
thesis A thesis (: theses), or dissertation (abbreviated diss.), is a document submitted in support of candidature for an academic degree or professional qualification presenting the author's research and findings.International Standard ISO 7144: D ...
entitled "Linear Functionals on Non-Locally Convex Spaces" under the supervision of
Allen Shields Allen Lowell Shields (May 7, 1927 – September 16, 1989) was an American mathematician who worked on measure theory, complex analysis, functional analysis and operator theory, and was "one of the world's leading authorities on spaces of analyti ...
in 1969 at the
University of Michigan The University of Michigan (U-M, U of M, or Michigan) is a public university, public research university in Ann Arbor, Michigan, United States. Founded in 1817, it is the oldest institution of higher education in the state. The University of Mi ...
. Upon graduating, he became a research associate at
Queen's University, Canada Queen's University at Kingston, commonly known as Queen's University or simply Queen's, is a public research university in Kingston, Ontario, Canada. Queen's holds more than of land throughout Ontario and owns Herstmonceux Castle in East Susse ...
, then from 1970 onwards was at
Michigan State University Michigan State University (Michigan State or MSU) is a public university, public Land-grant university, land-grant research university in East Lansing, Michigan, United States. It was founded in 1855 as the Agricultural College of the State o ...
, becoming a full
professor Professor (commonly abbreviated as Prof.) is an Academy, academic rank at university, universities and other tertiary education, post-secondary education and research institutions in most countries. Literally, ''professor'' derives from Latin ...
in 1979. He stayed at Michigan State until 2006, when he retired and became an adjunct professor at
Portland State University Portland State University (PSU) is a public research university in Portland, Oregon, United States. It was founded in 1946 as a post-secondary educational institution for World War II veterans. It evolved into a four-year college over the next ...
in
Oregon Oregon ( , ) is a U.S. state, state in the Pacific Northwest region of the United States. It is a part of the Western U.S., with the Columbia River delineating much of Oregon's northern boundary with Washington (state), Washington, while t ...
. Shapiro discovered some of the properties of
composition operator In mathematics, the composition operator C_\phi with symbol \phi is a linear operator defined by the rule C_\phi (f) = f \circ \phi where f \circ \phi denotes function composition. It is also encountered in composition of permutations in permutati ...
s, including a study of the cyclic properties of such operators 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 operator In mathematics, the composition operator C_\phi with symbol \phi is a linear operator defined by the rule C_\phi (f) = f \circ \phi where f \circ \phi denotes function composition. It is also encountered in composition of permutations in permutati ...
s on the
Hardy space In complex analysis, the Hardy spaces (or Hardy classes) H^p are spaces of holomorphic functions on the unit disk or upper half plane. They were introduced by Frigyes Riesz , who named them after G. H. Hardy, because of the paper . In real anal ...
s of the
Unit disc In mathematics, the open unit disk (or disc) around ''P'' (where ''P'' is a given point in the plane), is the set of points whose distance from ''P'' is less than 1: :D_1(P) = \.\, The closed unit disk around ''P'' is the set of points whose d ...
.


References


External links


Joel Shapiro's Homepage
Living people 20th-century American mathematicians 21st-century American mathematicians University of Michigan alumni Case Western Reserve University alumni Academic staff of Queen's University at Kingston Michigan State University faculty Portland State University faculty Year of birth missing (living people) {{US-mathematician-stub