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Isidore Isaac Hirschman Jr.

From Wikipedia, the free encyclopedia
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

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

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.