Allen Shields

{{Short description|American mathematician (1927–1989)}}

{{infobox scientist

| name = Allen Shields

| image = Allen Shields (1927–1989).jpeg

| birth_name = Allen Lowell Shields

| birth_date = {{birth date|1927|05|07}}

| birth_place = New York, U.S.

| death_date = {{death date and age|1989|09|16|1927|05|07}}

| death_place = Ann Arbor, Michigan, U.S.

| thesis_title = On Additive Properties of Real Numbers

| thesis_url = http://library.mit.edu/item/000686483

| thesis_year = 1952

| education = {{no wrap|City College of New York (BS)}}
Massachusetts Institute of Technology (PhD)

| doctoral_advisor = Witold Hurewicz

| fields = Mathematics

| workplaces = University of Michigan

| academic_advisors = Raphaël Salem

| doctoral_students = {{ubl|Theodore Kaczynski|Joel Shapiro|Russell Lyons}}

}}

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,{{Citation | last1=Duren | first1=Peter | title=In remembrance of Allen Shields | doi=10.1007/BF03023995 | mr=1044920 | year=1990 | journal=The Mathematical Intelligencer | issn=0343-6993 | volume=12 | issue=2 | pages=11–14| s2cid=122157471 }}{{citation

| last = Shapiro | first = Harold S.

| doi = 10.1007/BF03023994

| issue = 2

| journal = The Mathematical Intelligencer

| mr = 1044919

| pages = 8–10

| title = Allen Lowell Shields{{snd}}some reminiscences

| volume = 12

| year = 1990| s2cid = 120565153

}}{{MacTutor|id=Shields}}

and was "one of the world's leading authorities on spaces of analytic functions."{{citation

| last = Axler | first = Sheldon

| doi = 10.1007/BF03023992

| issue = 2

| journal = The Mathematical Intelligencer

| mr = 1044917

| page = 3

| title = Dedication

| volume = 12

| year = 1990}}

Shields was a student of Witold Hurewicz.{{mathgenealogy|id=7798}}

A special issue of The Mathematical Intelligencer, for which he served as editor of the "Years Ago" column, was dedicated to his memory in 1990.