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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. Mixed type PDEs and compressible flow

  2. Mixing time of random processes

  3. Noise-induced phenomena in stochastic heat equations

  4. Non-commutative Lp-spaces and analysis on quantum spaces

  5. Noncommutative Geometry. Quantum Space-Time and Diffeomorphism Invariant Geometry

  6. Noncommutative Surfaces

  7. Nonlocal generators of jump type Markov processes

  8. Normal form reduction for unconditional well-posedness of canonical dispersive equations

  9. Number theoretic results in a family

  10. On circle diffeomorphism groups

  11. On classification of long-term dynamics for some critical PDEs

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

  13. On Ingram’s Conjecture

  14. On some nonlinear elliptic problems

  15. On the distributions of partition ranks and cranks

  16. 15Apr
    by 김수현
    in 수학강연회

    On the resolution of the Gibbs phenomenon

  17. On the Schauder theory for elliptic PDEs

  18. One and Two dimensional Coulomb Systems

  19. Partial differential equations with applications to biology

  20. Periodic orbits in symplectic geometry

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