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]
Researchedit
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]
Selected publicationsedit
Articlesedit
——; Widder, D. V. (1949). "The inversion of a general class of convolution transforms". Transactions of the American Mathematical Society. 66: 135–201. doi:10.1090/S0002-9947-1949-0032817-4.
——; Widder, D. V. (1949). "A representation theory for a general class of convolution transforms". Transactions of the American Mathematical Society. 67: 69–97. doi:10.1090/S0002-9947-1949-0032818-6.
——; Jenkins, J. A. (1950). "Note on a result of Levine and Lifschitz". Proceedings of the American Mathematical Society. 1 (3): 390–393. doi:10.1090/S0002-9939-1950-0036346-7.
—— (1950). "Proof of a conjecture of I. J. Schoenberg". Proceedings of the American Mathematical Society. 1: 63–65. doi:10.1090/S0002-9939-1950-0032705-7.
——; Jenkins, J. A. (1950). "On lacunary Dirichlet series". Proceedings of the American Mathematical Society. 1 (4): 512–517. doi:10.1090/S0002-9939-1950-0036836-7.
—— (1950). "On the Behaviour of Fourier Transforms at Infinity and on Quasi-Analytic Classes of Functions". American Journal of Mathematics. 72 (1): 200–213. doi:10.2307/2372147. JSTOR 2372147.
——; Widder, D. V. (1951). "On the products of functions represented as convolution transforms". Proceedings of the American Mathematical Society. 2: 97–99. doi:10.1090/S0002-9939-1951-0041967-2.
—— (1952). "A convexity theorem for certain groups of transformations". Journal d'Analyse Mathématique. 2 (2): 209–218. doi:10.1007/BF02825637.
—— (1957). "Projections associated with Jacobi polynomials". Proceedings of the American Mathematical Society. 8 (2): 286–290. doi:10.1090/S0002-9939-1957-0085359-4.
Devinatz, A.; —— (1958). "The Spectra of Multiplier Transforms on ". American Journal of Mathematics. 80 (4): 829–842. doi:10.2307/2372836. ISSN 0002-9327. JSTOR 2372836.
Askey, Richard; —— (1959). "Weighted quadratic norms and ultraspherical polynomials. I". Transactions of the American Mathematical Society. 91 (2): 294–313. doi:10.1090/S0002-9947-1959-0107772-5.
—— (1959). "Weighted quadratic norms and ultraspherical polynomials. II". Transactions of the American Mathematical Society. 91 (2): 314–329. doi:10.1090/S0002-9947-1959-0107773-7.
—— (1960). "Hankel transforms and variation diminishing Kernels". Bulletin of the American Mathematical Society. 66: 40–43. doi:10.1090/S0002-9904-1960-10383-7.
—— (1962). "Multiplier transformations. III". Proceedings of the American Mathematical Society. 13 (6): 851–857. doi:10.1090/S0002-9939-1962-0143014-8.}
—— (1964). "Finite section Wiener-Hopf equations on a compact group with ordered dual". Bulletin of the American Mathematical Society. 70 (4): 508–511. doi:10.1090/S0002-9904-1964-11174-5.
Baxter, Glen; —— (1964). "An explicit inversion formula for finite-section Wiener-Hopf operators". Bulletin of the American Mathematical Society. 70 (6): 820–824. doi:10.1090/S0002-9904-1964-11248-9.
—— (1966). "Szegö functions on a locally compact Abelian group with ordered dual". Transactions of the American Mathematical Society. 121: 133–159. doi:10.1090/S0002-9947-1966-0190630-1.
—— (1966). "Errata to Szegö functions on a locally compact Abelian group with ordered dual". Transactions of the American Mathematical Society. 123 (2): 548. doi:10.1090/S0002-9947-66-99990-9.
——; Liang, D. S.; Wilson, E. N. (1982). "Szegő limit theorems for Toeplitz operators on compact homogeneous spaces". Transactions of the American Mathematical Society. 270 (2): 351–376. doi:10.1090/S0002-9947-1982-0645321-6.
Booksedit
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. ISBN978-0-88385-103-6.
Referencesedit
^ ab"Who's That Mathematician? Paul R. Halmos Collection – Page 23 | Mathematical Association of America". www.maa.org. Retrieved 2016-08-29.
^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.
^Hirschman, Isidore (2014-11-28). Infinite Series (Reprint ed.). Dover Publications Inc. ISBN9780486789750.
^Stenger, Allen (March 28, 2015). "Review of Infinite Series by Isidore Isaac Hirschman". MAA Reviews, Mathematical Association of America.
^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.
^Hirschman, Isidore Isaac; Widder, David Vernon (2012-05-04). The Convolution Transform. Courier Corporation. ISBN9780486154565.
isidore, isaac, hirschman, 1922, 1990, american, mathematician, professor, washington, university, louis, working, analysis, isidore, isaac, hirschmanborn, 1922, november, 1922diedjune, 1990, 1990, aged, nationalityamericanalma, materharvardscientific, careerf. Isidore Isaac Hirschman Jr 1922 1990 was an American mathematician and professor at Washington University in St Louis working on analysis Isidore Isaac HirschmanBorn 1922 11 22 November 22 1922DiedJune 10 1990 1990 06 10 aged 67 NationalityAmericanAlma materHarvardScientific careerFieldsHarmonic analysisOperator theoryInstitutionsWashington UniversityThesisSome Representation and Inversion Problems for the Laplace Transform 1947 Doctoral advisorDavid Widder Contents 1 Life 2 Research 3 Selected publications 3 1 Articles 3 2 Books 4 ReferencesLife editHirschman 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 editHirschman 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 n n displaystyle n times n nbsp 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 n displaystyle n rightarrow infty nbsp 3 Selected publications editArticles edit Widder D V 1949 The inversion of a general class of convolution transforms Transactions of the American Mathematical Society 66 135 201 doi 10 1090 S0002 9947 1949 0032817 4 Widder D V 1949 A representation theory for a general class of convolution transforms Transactions of the American Mathematical Society 67 69 97 doi 10 1090 S0002 9947 1949 0032818 6 Jenkins J A 1950 Note on a result of Levine and Lifschitz Proceedings of the American Mathematical Society 1 3 390 393 doi 10 1090 S0002 9939 1950 0036346 7 1950 Proof of a conjecture of I J Schoenberg Proceedings of the American Mathematical Society 1 63 65 doi 10 1090 S0002 9939 1950 0032705 7 Jenkins J A 1950 On lacunary Dirichlet series Proceedings of the American Mathematical Society 1 4 512 517 doi 10 1090 S0002 9939 1950 0036836 7 1950 On the Behaviour of Fourier Transforms at Infinity and on Quasi Analytic Classes of Functions American Journal of Mathematics 72 1 200 213 doi 10 2307 2372147 JSTOR 2372147 Widder D V 1951 On the products of functions represented as convolution transforms Proceedings of the American Mathematical Society 2 97 99 doi 10 1090 S0002 9939 1951 0041967 2 1952 A convexity theorem for certain groups of transformations Journal d Analyse Mathematique 2 2 209 218 doi 10 1007 BF02825637 1957 Projections associated with Jacobi polynomials Proceedings of the American Mathematical Society 8 2 286 290 doi 10 1090 S0002 9939 1957 0085359 4 Devinatz A 1958 The Spectra of Multiplier Transforms on ℓ p displaystyle ell p nbsp American Journal of Mathematics 80 4 829 842 doi 10 2307 2372836 ISSN 0002 9327 JSTOR 2372836 Askey Richard 1959 Weighted quadratic norms and ultraspherical polynomials I Transactions of the American Mathematical Society 91 2 294 313 doi 10 1090 S0002 9947 1959 0107772 5 1959 Weighted quadratic norms and ultraspherical polynomials II Transactions of the American Mathematical Society 91 2 314 329 doi 10 1090 S0002 9947 1959 0107773 7 1959 On multiplier transformations Duke Mathematical Journal 26 2 221 242 doi 10 1215 S0012 7094 59 02623 7 1960 Variation diminishing Hankel transforms Journal d Analyse Mathematique 8 307 336 doi 10 1007 BF02786854 hdl 2027 mdp 39015095257633 S2CID 120347146 1960 Hankel transforms and variation diminishing Kernels Bulletin of the American Mathematical Society 66 40 43 doi 10 1090 S0002 9904 1960 10383 7 1962 Multiplier transformations III Proceedings of the American Mathematical Society 13 6 851 857 doi 10 1090 S0002 9939 1962 0143014 8 Askey Richard 1963 Mean Summability for Ultraspherical Polynomials Mathematica Scandinavica 12 2 167 177 doi 10 7146 math scand a 10680 JSTOR 24489384 1964 Finite section Wiener Hopf equations on a compact group with ordered dual Bulletin of the American Mathematical Society 70 4 508 511 doi 10 1090 S0002 9904 1964 11174 5 Baxter Glen 1964 An explicit inversion formula for finite section Wiener Hopf operators Bulletin of the American Mathematical Society 70 6 820 824 doi 10 1090 S0002 9904 1964 11248 9 1966 Szego functions on a locally compact Abelian group with ordered dual Transactions of the American Mathematical Society 121 133 159 doi 10 1090 S0002 9947 1966 0190630 1 1966 Errata to Szego functions on a locally compact Abelian group with ordered dual Transactions of the American Mathematical Society 123 2 548 doi 10 1090 S0002 9947 66 99990 9 Liang D S Wilson E N 1982 Szego limit theorems for Toeplitz operators on compact homogeneous spaces Transactions of the American Mathematical Society 270 2 351 376 doi 10 1090 S0002 9947 1982 0645321 6 Books edit Hirschman I 1962 Infinite Series New York Holt Rinehart amp 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 edit a b Who s That Mathematician Paul R Halmos Collection Page 23 Mathematical Association of America www maa org Retrieved 2016 08 29 a b c Askey biography www groups dcs st andrews ac uk Retrieved 2016 08 29 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 Hirschman Isidore 2014 11 28 Infinite Series Reprint ed Dover Publications Inc ISBN 9780486789750 Stenger Allen March 28 2015 Review of Infinite Series by Isidore Isaac Hirschman MAA Reviews Mathematical Association of America 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 Hirschman Isidore Isaac Widder David Vernon 2012 05 04 The Convolution Transform Courier Corporation ISBN 9780486154565 Isidore Isaac Hirschman Jr at the Mathematics Genealogy Project http mathdl maa org mathDL 46 pa content amp sa viewDocument amp nodeId 3801 amp bodyId 4189 nbsp nbsp nbsp This article about an American mathematician is a stub You can help Wikipedia by expanding it vte Retrieved from https en wikipedia org w index php title Isidore Isaac Hirschman Jr amp oldid 1179839697, wikipedia, wiki, book, books, library,
