week 35: Basics on Fourier transform for absolutely and square-integrable functions, Poisson summation. STFT and its basic properties
week 36: Basic properties of the wavelet transform. Orthogonality relations and reconstruction formula for STFT and wavelet transform. Basics of Reproducing Kernel Hilbert Spaces (RKHS).
week 37:
week 38:
week 39:
week 40: Fundamental Identity of Gabor analysis, Wexler-Raz biorthogonality relations, Janssen representation, characterization of dual Gabor atoms, density theorem, Gaussian Gabor frames.
week 41: Duality theory of Gabor frames, Riesz bases, Riesz basic sequences, Bessel duality and some consequences.
week 42: Zak transform, Balian-Low theorem (Wiener amalgam version, classical version), Wiener amalgam spaces.
week 43: Localization operators, spectral properties
week 44:
week 45:
week 46: