Isidore Isaac Hirschman Jr.

Isidore Isaac Hirschman Jr. (1922–1990) was an American mathematician, and professor at Washington University in St. Louis working on analysis.

Isidore Isaac Hirschman
NationalityAmerican
Alma materHarvard
Scientific career
FieldsHarmonic analysis Operator theory
InstitutionsWashington University
ThesisSome Representation and Inversion Problems for the Laplace Transform (1947)
Doctoral advisorDavid Widder
InfluencedRichard Askey

Life

Hirschman earned his Ph.D. in 1947 from Harvard under David Widder. After writing ten papers together, Hirschman and Widder published a book entitled The Convolution Transform.[1] 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.[1] 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." [2]

Research

Hirschman's Ph.D. was entitled “Some Representation and Inversion Problems for the Laplace Transform,” He mainly published papers in harmonic analysis 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.[2] This was one of the two articles Hirschman and Askey co-wrote to complete Hirschman's 1955 research program.[2]

In 1964 Hirschman published Extreme eigen values of Toeplitz forms associated with Jacobi polynomials, showing that for banded Toeplitz matrices, eigenvalues accumulate on a spatial curve, in the complex plane with the normalized eigenvalue counting measure converging weakly to a measure on this curve as .[3]

Bibliography
  • Hirschman, I. (1962). Infinite Series. New York: Holt, Rinehart & Winston.[4] – 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.[5]
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References
  1. "Who's That Mathematician? Paul R. Halmos Collection – Page 23 | Mathematical Association of America". www.maa.org. Retrieved 2016-08-29.
  2. "Askey biography". www-groups.dcs.st-andrews.ac.uk. Retrieved 2016-08-29.
  3. Hirschman, I. I. (1964-01-01). "Extreme eigen values of Toeplitz forms associated with Jacobi polynomials". Pacific Journal of Mathematics. 14 (1): 107–161. ISSN 0030-8730.
  4. Hirschman, Isidore (2014-11-28). Infinite Series (Reprint ed.). Dover Publications Inc. ISBN 9780486789750.
  5. Hirschman, Isidore Isaac; Widder, David Vernon (2012-05-04). The Convolution Transform. Courier Corporation. ISBN 9780486154565.


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