https://www.math.snu.ac.kr/board/files/attach/images/701/ff97c54e6e21a4ae39315f9a12b27314.png
Extra Form
강연자 정재훈
소속 SUNY Buffalo
date 2016-04-07

Since Fourier introduced the Fourier series to solve the heat equation, the Fourier or polynomial approximation has served as a useful tool in solving various problems arising in industrial applications. If the function to approximate with the finite Fourier series is smooth enough, the error between the function and the approximation decays uniformly. If, however, the function is nonperiodic or has a jump discontinuity, the approximation becomes oscillatory near the jump discontinuity and the error does not decay uniformly anymore. This is known as the Gibbs-Wilbraham phenomenon. The Gibbs phenomenon is a theoretically well-understood simple phenomenon, but its resolution is not and thus has continuously inspired researchers to develop theories on its resolution. Resolving the Gibbs phenomenon involves recovering the uniform convergence of the error while the Gibbs oscillations are well suppressed. This talk explains recent progresses on the resolution of the Gibbs phenomenon focusing on the discussion of how to recover the uniform convergence from the Fourier partial sum and its numerical implementation. There is no best methodology on the resolution of the Gibbs phenomenon and each methodology has its own merits with differences demonstrated when implemented. This talk also explains possible issues when the methodology is implemented numerically. The talk is intended for a general audience.


  1. Fixed points of symplectic/Hamiltonian circle actions

  2. A modified separation method to solve a heat-transfer boundary value problem

  3. Arithmetic of elliptic curves

  4. <학부생을 위한 ɛ 강연> Convergence of Fourier series and integrals in Lebesgue spaces

  5. Trends to equilibrium in collisional rarefied gas theory

  6. The Lagrange and Markov Spectra of Pythagorean triples

  7. A-infinity functor and topological field theory

  8. Weak and strong well-posedness of critical and supercritical SDEs with singular coefficients

  9. Algebraic surfaces with minimal topological invariants

  10. A wrapped Fukaya category of knot complement and hyperbolic knot

  11. Alice and Bob meet Banach and von Neumann

  12. Congruences between modular forms

  13. W-algebras and related topics

  14. On function field and smooth specialization of a hypersurface in the projective space

  15. <학부생을 위한 ɛ 강연> 기하와 대수의 거울대칭

  16. 1 is big enough to understand 3

  17. Mathemaics & Hedge Fund

  18. Unique ergodicity for foliations

  19. Conformal field theory in mathematics

  20. <학부생을 위한 ɛ 강연> A mathematical approach to xEV battery system

Board Pagination Prev 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Next
/ 15