富氏分析一   (90年度 上學期)

I. Some topics from Fourier analysis on the circle and on the line: Fourier series for fuctions in L^2[0,1], Hilbert space, Fourier integrals for functions in Schwartz class and L^2(R), Paley- Wiener theorem, Wiener-Hopf factorization, etc. II. Applications: Applications in basic partial differential equations, the Poisson summation formula, Heisenbergs inequality, band- limited and time-limited signals, Shannon's sampling theorem, etc. III. Basic introduction to Wavelet analysis 上學期主要為上述Fourier級數、積分及其應用，預計下學期 主要的內容為：Wavelet analysis and the applications.

References: 1. H. Dym and H. P. Mckean, Fourier series and integrals, Academic Press, 1972. 2. I. Daubechies, Ten lectures on wavelets, SIAM, 1992. 3. G. Kaiser, A friendly guide to wavelets, Birkhauser, 1994. 4. J. -P. Kahane, and P.G. Lemarie'-Rieusset, S'eries de Fourier et Ondelettes, Cassini.

預備知識：高微、複變。（歡迎大三以上學生或研究生選修）