James Alexander Shohat

James Alexander Shohat (aka Jacques Chokhate (or Chokhatte), 18 November 1886, Brest-Litovsk – 8 October 1944, Philadelphia) was a Russian-American mathematician at the University of Pennsylvania who worked on the moment problem.[1] He studied at the University of Petrograd and married the physicist Nadiascha W. Galli, the couple emigrating from Russia to the United States in 1923.[1]

He was an Invited Speaker of the ICM in 1924 at Toronto.[2]

Selected works

"On a general formula in the theory of Tchebycheff polynomials and its applications". Trans. Amer. Math. Soc. 29 (3): 569–583. 1927. doi:10.1090/s0002-9947-1927-1501405-8. MR 1501405.
"A simple method for normalizing Tchebycheff polynomials and evaluating the elements of the allied continued fractions". Bull. Amer. Math. Soc. 33 (4): 427–432. 1927. doi:10.1090/s0002-9904-1927-04396-8. MR 1561395.
with J. Sherman: "On the numerators of the continued fraction". Proc Natl Acad Sci U S A. 18 (3): 283–287. 1932. doi:10.1073/pnas.18.3.283. PMC 1076208. PMID 16587678.
"On the development of functions in a series of polynomials". Bull. Amer. Math. Soc. 41 (2): 49–82. 1935. doi:10.1090/s0002-9904-1935-06007-0. MR 1563024.
"Mechanical quadratures, in particular, with positive coefficients". Trans. Amer. Math. Soc. 42 (3): 461–496. 1937. doi:10.1090/s0002-9947-1937-1501930-6. MR 1501930.[3]
"A differential equation for orthogonal polynomials". Duke Math. J. 5 (2): 401–417. 1939. doi:10.1215/s0012-7094-39-00534-x. MR 1546133.[4]
with J. D. Tamarkin: The problem of moments. Mathematical Surveys, vol. 1. New York: AMS. 1943. OCLC 622772715.[5]
"On van der Pol's and non-linear differential equations". J. Appl. Phys. 15 (7): 568–574. 1944. doi:10.1063/1.1707470.[6]

References

Kline, J. R. (3 November 1944). "Obituary: James Alexander Shohat". Science. 100 (2601): 397–398. doi:10.1126/science.100.2601.397.
Shohat, J. A. "On the asymptotic properties of a certain class of Tchebycheff polynomials." Archived 2017-12-01 at the Wayback Machine In Proc. Intern. Math. Congress Toronto, pp. 611–618. 1924.
18 Aug. 2012 email from R. Askey: "I suspect that "On mechanical quadratures, in particular, with positive coefficients", Trans AMS 42 (1937), 461-496 is the most important paper among those dealing with interpolation and quadrature, but I am not an expert on this and have not read enough to be sure."
18 Aug. 2012 email from R. Askey: "I am not an expert on all of Shohat's work, but I think the most important paper is: A differential equation for orthogonal polynomials, Duke Math Journal, 5(1939)401-417. In it he finds a difference equation for a coefficient in the recurrence relation for polynomials orthogonal on the real line with respect to e^(-x^4). It turns out that this nonlinear difference equation is a discrete analogue of one of the Painleve differential equations, and I think the first discrete Painleve equation found."
Widder, D. V. (1945). "Review: J. A. Shohat and J. D. Tamarkin, The problem of moments". Bull. Amer. Math. Soc. 51 (11): 860–863. doi:10.1090/s0002-9904-1945-08459-6.
18 Aug. 2012 email from R. Askey: "Norman Levinson give the following paper a very strong review. On van der Pol's and non-linear differential equations, J. Appl. Phys15 (1944), 568-574 [along with giving a very strong negative comment on Shohat's earlier paper on von der Pol's equation]."

External links

James Alexander Shohat at the Mathematics Genealogy Project

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[obit-1] Kline, J. R. (3 November 1944). "Obituary: James Alexander Shohat". Science. 100 (2601): 397–398. doi:10.1126/science.100.2601.397.

[2] Shohat, J. A. "On the asymptotic properties of a certain class of Tchebycheff polynomials." Archived 2017-12-01 at the Wayback Machine In Proc. Intern. Math. Congress Toronto, pp. 611–618. 1924.

[3] 18 Aug. 2012 email from R. Askey: "I suspect that "On mechanical quadratures, in particular, with positive coefficients", Trans AMS 42 (1937), 461-496 is the most important paper among those dealing with interpolation and quadrature, but I am not an expert on this and have not read enough to be sure."

[4] 18 Aug. 2012 email from R. Askey: "I am not an expert on all of Shohat's work, but I think the most important paper is: A differential equation for orthogonal polynomials, Duke Math Journal, 5(1939)401-417. In it he finds a difference equation for a coefficient in the recurrence relation for polynomials orthogonal on the real line with respect to e^(-x^4). It turns out that this nonlinear difference equation is a discrete analogue of one of the Painleve differential equations, and I think the first discrete Painleve equation found."

[5] Widder, D. V. (1945). "Review: J. A. Shohat and J. D. Tamarkin, The problem of moments". Bull. Amer. Math. Soc. 51 (11): 860–863. doi:10.1090/s0002-9904-1945-08459-6.

[6] 18 Aug. 2012 email from R. Askey: "Norman Levinson give the following paper a very strong review. On van der Pol's and non-linear differential equations, J. Appl. Phys15 (1944), 568-574 [along with giving a very strong negative comment on Shohat's earlier paper on von der Pol's equation]."