Harmonic Analysis and Applications

​Michael Th. Rassias is a Research Fellow at the University of Zürich, a visiting researcher at the Institute for Advanced Study, Princeton, as well as a visiting Associate Professor at the Moscow Institute of Physics and Technology. He obtained his PhD in Mathematics from ETH-Zürich in 2014. During the academic year 2014-2015, he was a Postdoctoral researcher at the Department of Mathematics of Princeton University and the Department of Mathematics of ETH-Zürich, conducting research at Princeton. While at Princeton, he prepared with John F. Nash, Jr. the volume "Open Problems in Mathematics", Springer, 2016. He has received several awards in mathematical problem-solving competitions, including a Silver medal at the International Mathematical Olympiad of 2003 in Tokyo. He has authored and edited several books with Springer. His current research interests lie in mathematical analysis, analytic number theory, and more specifically the Riemann Hypothesis, Goldbach’s conjecture, thedistribution of prime numbers, approximation theory, functional equations and analytic inequalities.

“It might serve as the foundation for the occasional graduate topics course in harmonic analysis. Many of the contributed chapters present new results and most provide a thoughtful introduction along with sufficient references to orient readers unfamiliar with the relevant subfield.” (Brody Johnson, MAA Reviews, October 3, 2021)

• Sampling and Approximation in Shift Invariant subspaces of L2(ℝ) (Atreas).- Optimal ℓ1 rank one matrix decomposition (Balan).- An arithmetical function related to Báez-Duarte’s criterion for the Riemann hypothesis (Balazard).- Large Sets Avoiding Rough Patterns (Zahl).- PDE methods in Random Matrix Theory (Hall).- Structure and optimisation in computational harmonic analysis –  On key aspects in sparse regularisation (Hansen).- Reflections on a Theorem of Boas and Pollard (Heil).- The Andoni-Krauthgamer-Razenshteyn characterization of sketchable norms fails for sketchable metrics (Noar).- Degree of convergence of some operators ^ 1 (Mohapatra).- Real variable methods in harmonic analysis and Navier–Stokes equations (Lemarié-Rieusset).- Explore intrinsic geometry of sleep dynamics and predict sleep stage by unsupervised learning techniques (Wu).- Harmonic functions in slabs and half-spaces (Madych).