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Allen Shields was an undergraduate at the City College New York where his lecturers included Emil Post and Lee Lorch. His doctoral studies were at M.I.T. under Witold Hurewicz's supervision and he received his doctorate in 1952. Despite the fact that Hurewicz was his official supervisor, Shields was unofficially supervised by Raphaël Salem who, at that time, was half the time in Paris and half in M.I.T.
Shields' first post was at Tulane where he learnt a lot of functional analysis and wrote papers on topological semigroups. He was appointed to Ann Arbor in 1955 and remained there except for two years (1959-61) spent in New York.
Shields worked on a wide range of mathematical topics including measure theory, complex functions, functional analysis and operator theory. F W Gehring described his work in these words
Allen's standards were high, his taste impeccable, and his ideas deep. He was one of the world's most versatile practitioners in the art of applying functional analysis to gain insight on and solve problems of classical function theory. He had a profound effect on the development of this subject through his research and his personal contacts with colleagues and students.
Article by: J J O'Connor and E F Robertson
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