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.

List of Articles
카테고리 제목 소속 강연자
수학강연회 Noise-induced phenomena in stochastic heat equations file 포항공대 김건우
수학강연회 Non-commutative Lp-spaces and analysis on quantum spaces file 서울대학교 이훈희
수학강연회 Noncommutative Geometry. Quantum Space-Time and Diffeomorphism Invariant Geometry file 서울대학교 Raphael Ponge
수학강연회 Noncommutative Surfaces file 서강대학교 Jens Hoppe
수학강연회 Nonlocal generators of jump type Markov processes file University of Bielefeld Walter Hoh
수학강연회 Normal form reduction for unconditional well-posedness of canonical dispersive equations file KAIST 권순식
수학강연회 Number theoretic results in a family file Univ. of Toronto / KIAS Kim, Henry
수학강연회 On circle diffeomorphism groups file 고등과학원 김상현
수학강연회 On function field and smooth specialization of a hypersurface in the projective space file KAIST 이용남
수학강연회 On Ingram’s Conjecture file University of Zagrab Sonja Stimac
수학강연회 On some nonlinear elliptic problems file Paul Sabatier University, Toulouse Yuri Egorov
수학강연회 On the distributions of partition ranks and cranks file 서울과학기술대학교 김병찬
수학강연회 On the resolution of the Gibbs phenomenon file SUNY Buffalo 정재훈
수학강연회 On the Schauder theory for elliptic PDEs file 연세대학교 김세익
수학강연회 One and Two dimensional Coulomb Systems file 카이스트 폴정
수학강연회 Partial differential equations with applications to biology file POSTECH 황형주
수학강연회 Periodic orbits in symplectic geometry file 서울대 강정수
수학강연회 Q-curvature in conformal geometry file 서강대 Pak Tung Ho
수학강연회 Quantitative residual non-vanishing of special values of various L-functions file UNIST 선해상
수학강연회 Quantum Dynamics in the Mean-Field and Semiclassical Regime file Ecole Polytechnique Francoise Golse
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