James Alexander Shohat Explained
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.. 1927. 29. 3. 569–583. 1501405. 10.1090/s0002-9947-1927-1501405-8. free. Shohat. J..
- A simple method for normalizing Tchebycheff polynomials and evaluating the elements of the allied continued fractions. Bull. Amer. Math. Soc.. 1927. 33. 4. 427–432. 1561395. 10.1090/s0002-9904-1927-04396-8. free. Shohat. J. A..
- with J. Sherman: On the numerators of the continued fraction. Proc Natl Acad Sci U S A. 1932. 18. 3. 283–287. 1076208. 10.1073/pnas.18.3.283. 16587678. free. Shohat. J.. Sherman. J..
- On the development of functions in a series of polynomials. Bull. Amer. Math. Soc.. 1935. 41. 2. 49–82. 1563024. 10.1090/s0002-9904-1935-06007-0. free.
- Mechanical quadratures, in particular, with positive coefficients. Trans. Amer. Math. Soc.. 1937. 42. 3. 461–496. 1501930. 10.1090/s0002-9947-1937-1501930-6. free. Shohat. J.. [3]
- A differential equation for orthogonal polynomials. Duke Math. J.. 1939. 5. 2. 401–417. 1546133. 10.1215/s0012-7094-39-00534-x. Shohat. J.. [4]
- with J. D. Tamarkin: Book: The problem of moments. Mathematical Surveys, vol. 1. 1943. New York. AMS. 622772715. [5]
- On van der Pol's and non-linear differential equations. J. Appl. Phys.. 1944. 15. 7. 568–574. 10.1063/1.1707470. [6]
See also
Notes and References
- Kline, J. R.. John Robert Kline. Obituary: James Alexander Shohat. Science. 3 November 1944 . 100. 2601. 397–398. 10.1126/science.100.2601.397. 17799450.
- Shohat, J. A. "On the asymptotic properties of a certain class of Tchebycheff polynomials." 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, DukeMath 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.. David Widder. Review: J. A. Shohat and J. D. Tamarkin, The problem of moments. Bull. Amer. Math. Soc.. 1945. 51. 11. 860–863. 10.1090/s0002-9904-1945-08459-6. free.
- 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]."