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
Born(1922-11-22)November 22, 1922
DiedJune 10, 1990(1990-06-10) (aged 67)
NationalityAmerican
Alma materHarvard
Scientific career
FieldsHarmonic analysis
Operator theory
InstitutionsWashington University
Thesis Some Representation and Inversion Problems for the Laplace Transform  (1947)
Doctoral advisorDavid Widder

Life

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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, publishing 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

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Hirschman's PhD 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, 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 eigenvalues 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]

Selected publications

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Articles

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Books

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  • Hirschman, I. (1962). Infinite Series. New York: Holt, Rinehart & Winston.[4] – A textbook for advanced undergraduate and graduate mathematics.[5]
  • Hirschman, Isidore Isaac; Widder, David Vernon (1955). The Convolution Transform. New York: Princeton University Press;[6] now available from Dover Publications.[7]
  • Hirschman, I. I., ed. (1965). Studies in Real and Complex Analysis. Mathematical Association of America. ISBN 978-0-88385-103-6.

References

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  1. ^ a b "Who's That Mathematician? Paul R. Halmos Collection – Page 23 | Mathematical Association of America". www.maa.org. Retrieved 2016-08-29.
  2. ^ a b c "Askey biography". www-groups.dcs.st-andrews.ac.uk. Archived from the original on 2016-09-11. 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. doi:10.2140/pjm.1964.14.107. ISSN 0030-8730.
  4. ^ Hirschman, Isidore (2014-11-28). Infinite Series (Reprint ed.). Dover Publications Inc. ISBN 9780486789750.
  5. ^ Stenger, Allen (March 28, 2015). "Review of Infinite Series by Isidore Isaac Hirschman". MAA Reviews, Mathematical Association of America.
  6. ^ Blackman, Jerome (1957). "Book Review: The convolution transform". Bulletin of the American Mathematical Society. 63 (3): 205–208. doi:10.1090/S0002-9904-1957-10106-2. ISSN 0002-9904.
  7. ^ Hirschman, Isidore Isaac; Widder, David Vernon (2012-05-04). The Convolution Transform. Courier Corporation. ISBN 9780486154565.