Computational Time-Frequency and Coorbit Theory

Explore advanced mathematical concepts in this comprehensive lecture series on computational time-frequency analysis and coorbit theory. Delve into the mathematical foundations and applications of function spaces, atomic decompositions, and their connections to various areas of mathematics and applied sciences. Master the theoretical framework of coorbit theory and its extensions into group representation theory, complex analysis, and practical applications. Examine frame theory from both mathematical and numerical perspectives, covering wavelets, shearlets, and geometric frames. Investigate time-frequency frames and their applications to audio analysis, including modulation spaces and their relationship to Gabor expansions. Study the connections between these mathematical structures and slowly varying channels in mobile communication modeling. Analyze pseudo-differential operators belonging to the Sjoestrand class and their descriptions through modulation spaces. Learn about wavelet theory, coorbit spaces, and their ramifications in modern analysis. Explore specialized topics including products of Toeplitz operators on the Fock space, analytic continuation of Toeplitz operators, and Hankel and composition operators on spaces of Dirichlet series. Gain insights into how these mathematical tools provide solutions with minimal computational costs while achieving optimal approximation behavior in various function spaces.