Mathematical Tools for the Detection and Analysis of Local Singularities - Lecture 3

Explore advanced mathematical techniques for detecting and analyzing local singularities in signals during this third lecture in a series. Delve into the application of wavelet bases, Wilson bases, and related tools to characterize pointwise singularities in various fields such as turbulence, gravitational waves, and physiological data. Learn about the classification of singularities using the p-exponent of Calderón and Zygmund and fractional integration. Discover how to perform multifractal analysis to estimate fractional dimensions of sets with specific pointwise regularity exponents. Examine the extension of these techniques to wider settings and non-pointwise singularities, including the analysis of "chirps" in gravitational waves using time-frequency analysis methods like Wilson or Malvar bases and redundant decomposition systems.

Stéphane Jaffard: Mathematical tools for the detection and analysis of local singularities... III