Description: Prereq- uisite(s): MATH 146C, MATH 165B, MATH 209C; or consent of instructor. A study of Fourier series. Includes summability methods, kernels, Fourier transform, unitarity, applications to the uncertain- ty principle, and distributional Fourier transform. Introduces Hardy spaces, singular integral operators, and wavelet theory and its applications. Other topics include interpolation of linear operators and spectral analysis and applications.