Isidore Isaac Hirschman Jr. (1922–1990) was an American mathematician, and professor at
Washington University in St. Louis
Washington University in St. Louis (WashU or WUSTL) is a private research university with its main campus in St. Louis County, and Clayton, Missouri. Founded in 1853, the university is named after George Washington. Washington University is r ...
working on
analysis
Analysis ( : analyses) is the process of breaking a complex topic or substance into smaller parts in order to gain a better understanding of it. The technique has been applied in the study of mathematics and logic since before Aristotle (38 ...
.
Life
Hirschman earned his Ph.D. in 1947 from Harvard under
David Widder
David Vernon Widder (25 March 1898 – 8 July 1990) was an American mathematician. He earned his Ph.D. at Harvard University in 1924 under George Birkhoff and went on to join the faculty there.
He was a co-founder of the ''Duke Mathematical Jour ...
. After writing ten papers together, Hirschman and
Widder published a book entitled ''
The Convolution Transform''.
Hirschman spent most of his career (1949–1978) at Washington University, where he published mainly in harmonic analysis and operator theory. Washington University holds a lecture series given by Hirschman, with one lecture given by Richard Askey.
While Askey was at Washington University, Hirschman asked him to solve an ultraspherical polynomial problem. Askey says in this lecture, "This led to a joint paper, and was what started my interest in special functions."
Research
Hirschman's Ph.D. was entitled “Some Representation and Inversion Problems for the Laplace Transform,” He mainly published papers in
harmonic analysis
Harmonic analysis is a branch of mathematics concerned with the representation of Function (mathematics), functions or signals as the Superposition principle, superposition of basic waves, and the study of and generalization of the notions of Fo ...
and
operator theory. In 1959 Hirschman wrote a paper with Askey, ''Weighted quadratic norms and ultraspherical polynomials'', which was published in the ''Transactions of the American Mathematical Society''.
This was one of the two articles Hirschman and Askey co-wrote to complete Hirschman's 1955 research program.
In 1964 Hirschman published ''Extreme eigen values of Toeplitz forms associated with Jacobi polynomials'', showing that for
banded
Toeplitz matrices In linear algebra, a Toeplitz matrix or diagonal-constant matrix, named after Otto Toeplitz, is a matrix in which each descending diagonal from left to right is constant. For instance, the following matrix is a Toeplitz matrix:
:\qquad\begin
a & b ...
,
eigenvalues
In linear algebra, an eigenvector () or characteristic vector of a linear transformation is a nonzero vector that changes at most by a scalar factor when that linear transformation is applied to it. The corresponding eigenvalue, often denoted b ...
accumulate on a spatial curve, in the
complex plane
In mathematics, the complex plane is the plane formed by the complex numbers, with a Cartesian coordinate system such that the -axis, called the real axis, is formed by the real numbers, and the -axis, called the imaginary axis, is formed by the ...
with the normalized eigenvalue counting measure converging weakly to a measure on this curve as
.
Selected publications
Articles
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Books
* Hirschman, I. (1962). ''Infinite Series.'' New York'':'' Holt, Rinehart & Winston. – A textbook for advanced undergraduate and graduate mathematics.
*Hirschman, Isidore Isaac; Widder, David Vernon (1955). ''The Convolution Transform.'' New York: Princeton University Press;
now available from Dover Publications.
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References
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*http://mathdl.maa.org/mathDL/46/?pa=content&sa=viewDocument&nodeId=3801&bodyId=4189
20th-century American mathematicians
Harvard University alumni
Washington University in St. Louis faculty
Washington University in St. Louis mathematicians
1922 births
1990 deaths
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