Người trình bày: Gs. Tom H. Koornwinder, trường đại học Amsterdam
Địa điểm: Phòng 301, nhà A5
Thời gian: 9:30-11:30
Tóm tắt: This survey lecture (joint work with Enno Diekema, see [2]) discusses the history of approximation formulas for n-th order derivatives by integrals involving orthogonal polynomials. There is a large but rather disconnected corpus of literature on such formulas. The pioneers, who worked independently of each other, are Cioranescu (1938), Haslam-Jones (1953), Lanczos (1956) and Savitzky & Golay (1964). Applications which motivated these formulas are as diverse as numerical mathematics, spectroscopy, electrical engineering, filter theory and actuarial science. I will somewhat generalize the various results in literature, in particular unifying the continuous and discrete case. Many side remarks will be made, for instance on wavelets, Mantica's Fourier-Bessel functions, Greville's minimum $R_alpha$ formulas in connection with discrete smoothing, and the incredible history of an identity incorrectly ascribed in [1] to Chaundy & Bullard.
[1] T.H. Koornwinder and M.J. Schlosser, On an identity by Chaundy and Bullard. I, Indag. Math. (N.S.) 19 (2008), 239-261; arXiv:0712.2125v3.
[2] E. Diekema and T.H. Koornwinder, Differentiation by integration using orthogonal polynomials, a survey, arXiv:1102.5219v1. |
