Joseph L. Walsh

Joseph L. Walsh ( Joseph Leonard "Joe" Walsh; born September 21, 1895 in Washington, DC , † December 6, 1973 in College Park , Maryland ) was an American mathematician who mainly worked in analysis .

life and work

Joseph L. Walsh graduated from Harvard University . He completed his studies first in 1916 with a BS and, after a time in the US Navy during World War I, finally in 1920 with a doctorate from Maxime Bôcher . He then worked as a lecturer at Harvard and studied on research grants for one year in Paris under Paul Montel (1920–1921) and in Munich under Constantin Carathéodory (1925–1926).

From 1935 he was a full professor at Harvard University, where he was faculty director from 1937 to 1942. In the Second World War he served again as an officer in the US Navy (as Lieutenant Commander, after the war he was promoted to Captain). After his retirement from Harvard in 1966, he was active as a professor at the University of Maryland until a few weeks before his death.

His work focused on theorems about the mutual position of the critical points (zeros of the derivatives) and zeros of polynomials and Greens functions (harmonic functions) and the theory of interpolation and approximation of functions, where he generalized, for example, the theorems of Weierstrass and Runge about polynomial approximations . His generalizations are now special cases (in one or two dimensions) of a theorem by Mergelyan : Let a function f be continuous on a closed bounded set S and be analytical for all inner points of S, then f on S can be approximated uniformly by polynomials.

The Walsh function and the Walsh code are named after him. He examined the orthonormal function systems known as Walsh functions (which consist of “rectangle” -shaped functions) in 1923 (American Journal of Mathematics vol. 45, p. 5). They are widely used today, for example in signal processing.

In 1929 Walsh was elected to the American Academy of Arts and Sciences . He became a member of the United States' National Academy of Sciences in 1936 . From 1949 to 1951 he was President of the American Mathematical Society .

Publications

• Interpolation and Approximation by rational functions in the complex domain. AMS Colloquium Publications, 1935; 5th edition 1969
• The location of critical points of analytic and harmonic functions. AMS Colloquium Publications, 1950
• with John Harold Ahlberg & Edwin Norman Nilson: The theory of Splines and their Applications. Academic Press, 1967, ISBN 0-12-044750-9

literature

• Morris Marden: Joseph L. Walsh in Memoriam. In: Bulletins of the American Mathematical Society. Volume 81, Issue 1, January 1975 ( PDF; 2.3 MB ). Bulletins of the American Mathematical Society, Volume 81, issue 1, January 1975

Web links

• Literature by and about Joseph L. Walsh in the catalog of the German National Library
• John J. O'Connor, Edmund F. Robertson :  Joseph L. Walsh. In: MacTutor History of Mathematics archive .