임경수 교수

Bio

He received the B.S. degree from Korea University (KU), Korea in 1990, the MS and Ph.D. degree in harmonic analysis of mathematics from Korea Advanced Institute of Science and Technology (KAIST), Korea in 1992 and 1996, respectively.

He is a full professor in the department of mathematics at Sogang University in Seoul, Korea and served as the Chair of Mathematics Department from 2013-15, the Dean of Administrations Affairs from 2015-17, and the Dean of Academic Affairs from 2017-18, and the Dean of Interdisciplinary Basic Education from 2017-18.

His recent research interests focus on the probabilistic machine intelligence related to the Koopman operator of dynamical systems including the continuity of convolution and compositions between function spaces.

Students

• 박사과정  윤경주 (인공지능대학원)
• 박사과정  Do Thi Minh Huyen (인공지능대학원)
• 석사과정  김태현 (인공지능대학원)
• 석사과정  송민정 (인공지능대학원)
• 석사과정  박성원 (대학원 수학과)
• 학부연구생  김민정 (경제학과)

Teaching

I am teaching two courses this semester. One is a course in mathematical statistics, taught at the level of a third-year mathematics major. The other is a course on Fourier analysis, which can be considered fairly challenging. However, it is designed so that second-year mathematics students can grasp the material through intuitive understanding rather than rigorous theory.

Research

My research area is classical harmonic analysis. I am primarily interested in the continuity properties of convolution operators, with a particular focus on the theory of distributions and statistical methodologies. More recently, I have been working on the problem of recovering distribution functions from random samples within dynamical systems. As an application of this work, I study independent component analysis without the assumption of non-Gaussianity. This line of research has potential applications in generative algorithms and probabilistic neural networks. Below, you will find my publications organized by type and year. For questions about any specific publication, please contact my office, and a member of the teaching staff will respond as soon as possible.

Articles

• Independent component analysis without gaussianity restriction (with K.J. Yoon), (2026) preprint.
• Bayesian analysis of option volatility (with Y.H. Kim), (2026) preprint.
• A Statistical Approach to estimating GWP from chemical properties (with S.W. Baek), (2026) preprint.
• Mid-IR ATR-FTIR with simple ML framework for PVC screening and polyethylene subclassification with perfect external validation (with Kang, Park, Lee), (2026) accepted.
• An algorithm for approximating implicit functions by polynomials without using higher order differentiability information, Numerical Algorithms, 98(3) (2024), 1261--1279.
• Variational non-Bayesian inference of the probability density function in the Wiener algebra (with U.J. Choi), (2023) preprint.
• Probabilistic neural network: Frequency and moment learnings (with U.J. Choi), (2020) preprint.
• Multivariate Bernstein inequalities for entire functions of exponential type in Lₚ(Rⁿ) (0<p<1), Jour. Ineq. and Appl. 215 (2019) 1--16.
• A weighted Fourier series with signed good kernels, Comm. Korean. Math. Soc., 54(3) (2017), 935--952.
• Gibbs phenomenon for Fourier partial sums on Zₚ, J. Math. Anal. Appl, 433(1) (2016), 392--404.
• A Weighted OFDM Signal Scheme for Peak-to-Average Power Ratio Reduction of OFDM Signals (with Shin, Kim) IEEE Trans. on Vehicular Technology, 62(3) (2013), 1406--1409.
• Local edge detectors using a sigmoidal transformation for piecewise smooth data (with B.I.Yoon), Applied Mathematics Letters 26 (2013), 270--276.
• Stability of localized integral operators on weighted Lₚ spaces (with Sun, Shin), Numer. Func. Anal. Optim., 7-9 (2012), 1,166--1,193.
• Fractional integrals over a function of finite type on the intersection spaces (with J. Nah), Jour. Math. Anal. Appl. 387(2) (2012), 1209--1218.
• Gibbs phenomenon removal by adding Heaviside functions (with B.I. Yoon), Adv. Comp. Math. (2011), 1--17.
• Norm inequalities for the conjugate operator in two-weighted Lebesgue spaces (with J. Lee), Jour. Inequl. Appl. 2011:117 (22 November 2011).
• Estimates of M-harmonic conjugate operator (with J. Lee), Jour. Ineq. Appl. 2010:435450 (30 March 2010).
• Construction of Lanczos type filters for the Fourier series approximation (with B. I. Yun), Appl. Numer. Math. 59 (2009), 280--300.
• Nonuniform sampling of bandlimited functions (with C. E. Shin, M. B. Lee), IEEE Trans. Inform. Theory 54 (2008), no. 8, 3814--3819.
• An algorithm to determine a dipole current in a sphere (with B. I. Yun, S. Y. Choung), Math. Methods in the Applied Science 30 (2007), 1105--1119.
• Estimates of weighted Hardy-Littlewood averages on the p-adic vector space (with J. Lee), J. Math. Anal. Appl. 324 (2006), 1470--1477.
• An averageing method for the Fourier approximation to discontinuous functions (with B. I. Yun), Applied Math. and Comp. 183 (2006), 272--284.
• Uniqueness of non-harmonic series under a weaker growth condition Integral Transform and Special Functions (with S. Y. Choung), 17(2006), 27--30.
• Green functions on the p-adic vector space (with J. W. Son), Comm. Kor. Math. Soc. 20(4) (2005), 657--669.
• Properties of symmetric matrices (with J. Lee), Jour. Math. Anal. and Appl. 305 (2005), 219--226.
• Estimates of Marcinkiewicz integrals with bounded homogeneous kernels of degree zero (with J. Lee), Integral Equations and Operator Theory 48 (2004), 213--223.
• Properties for M-harmonic conjugate operator (with J. Lee), Canadian Math. Bull. 46 (2003), 113--121.
• Mapping properties of the Marcinkiewicz integrals on homogeneous groups (with Y. Choe), Jour. Kor. Math. Soc. 39 (2002), 61--75.
• Marcinkiewicz integral operators on product domains, Math. Proc. Cambridge Philos. Soc. 132 (2002), 523--530.
• Weighted norm inequalities for pluriharmonic conjugate functions (with J. Lee), Jour. Math. Anal. and Appl. 268 (2002), 707--717.
• Maximal functions over hypersurfaces with flat points, Jour. Math. Anal. and Appl. 260(2001), 70--82.
• Marcinkiewicz integrals with rough kernels on Lₚ, Jour. Math. Anal. and Appl. 232 (1999), 347--358.
• Weighted norm inequalities for M-harmonic conjugate functions (with U. J. Choi), Complex Variables Theory and Appl. 34 (1997), 437--444.
• Fractional derivatives of Bloch functions, Growth rate, and interpolation (with B. R. Choe), Acta Math. Hung. 72 (1996), 67--86.

Recent Research Funds

• 2023.7 ~ 2030.12 OLED 디스플레이용 산화물 TFT 절연막 패턴 형성을 위한 150이하의 저온난화지수를 지니는 F기반 PFC 대체가스 개발 (한국산업기술평가관리원)
• 2017.9 ~ 2021.8 주가지표 분석을 위한 비균질 은닉 마르코프 모형의 수리적 연구 및 응용 (중견연구자과정, 연구재단)
• 2018.3.1 ~ 2021.6 과학교사 및 예비 과학교사 재교육 프로그램을 통한 캄보디아 과학기술 인력 (개도국지원사업, 연구재단)

Office Hours

Spring 2026 office hours are Monday (9:00~10:30, 17:10~17:40), Wednesday (9:00~10:30, 17:10~17:40), Tuesday (13:00~15:00), and Thursdays (13:00~15:00). Please email or request specific times with the form on SAINT.