Credits: 3 (3-0-0)
Description
Schauder bases in Banach spaces, Trigonometric system, Weak and weak* bases, Characterization of Schauder bases, duality of bases, perturbation of bases.
Absolute and unconditional convergence of series in a Banach space, Unconditional bases, Characterization, Scahuder basis for C([0,1]) and it’s unconditionality.
Besel sequences and Riesz bases in Hilbert spaces, Frames in a Hilbert space, Frame operator, Characterizations of frames, Frame series and its convergence.
Fourier transform of L^1 functions on R, convolution of L^1 functions and its Fourier transform, Plancherel theorem.
Band limited functions, Sampling theorem, Frames of translates, Time- frequency shifts, Painless nonorthogonal expansions, Nyquest density, Necessary conditions for frame bounds, Wiener amalgam spaces, Zak transform, Gabor systems at the critical density, Balian-low theorem.
Wavelet frames, Frame bounds, Admissibility criteria.