MTL750
| MTL750 | |
|---|---|
| Harmonic Analysis and Its Applications | |
| Credits | 3 |
| Structure | 3-0-0 |
| Pre-requisites | |
| Overlaps | |
MTL750 : Harmonic Analysis and Its Applications
[edit]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.