Pseudo-Differential Operators and Related Topics Extended Abstracts PSORT 2024

The current volume gives an update on recent developments in the theory of pseudo-differential operators and related topics. The results collected here were presented at the Pseudo-Differential Operators and Related Topics (PSORT) 2024 Conference at Ghent University, Belgium, and cover a wide range of topics in pseudo-differential operators, microlocal analysis, time-frequency analysis, and related applications.

- On the existence of a Weyl calculus on graded Lie groups.- On Courant and Pleijel theorems for sub-Riemannian Laplacians.- Fourier analysis on lattices and beyond.- Normal forms and regularity at radial points.- Fredholmness of pseudodifferential operators on rearrangement-invariant spaces.- Diophantine conditions and global properties for systems of vector fields in tori and spheres.- Phase space Feynman path integrals of parabolic type on the torus as analysis on path space.- Quasi-Clustering for the Spectrum of Semiregular Systems.- Multilinear Fourier integral operators on modulation spaces.- Pseudodifferential operators with completely periodic symbols and Gabor frames.- Characterization of wave front sets associated with ultradistributional spaces by special orbital wavelet transform.- Ridgelet transform on Gelfand-Shilov spaces of type W.- Recent advances in harmonic analysis on the group SL(2, R).- Pseudodifferential transmission problems.- Pseudo-differential operators involving the Weinstein transform.- Banach-space-valued ultradistributions involving the Weinstein transform.- Regularity of oscillatory integral operators arising in evolutionary PDEs, in classical function spaces.- Restriction theorems for Fourier-Dunkl transform.- On the iterates of the Laguerre operator.

Vishvesh Kumar earned his Ph.D. in Mathematics from the Indian Institute of Technology Delhi, India, in 2019. Currently, he is a postdoctoral researcher at the Ghent Analysis & PDE Center, Ghent University, Belgium. His research focuses on pseudo-differential operators, abstract harmonic analysis, and partial-differential equations on Lie groups and symmetric spaces. He has authored over 40 research articles published in several leading international journals. He is a life member of the International Society for Analysis, its Applications, and Computation (ISAAC).

David Rottensteiner earned his PhD from Imperial College London in 2014. Since then he has held postdoctoral positions at the University of Vienna, Austria, and Ghent University, Belgium. His research focuses on harmonic analysis and pseudo-differential operators on nilpotent Lie groups.

 Michael Ruzhansky is a Senior Full Professor of Mathematics at Ghent University in Belgium, and a Professor of Mathematics at Queen Mary University of London in the United Kingdom. His research interests mainly lie in Partial Differential Equations, Microlocal and Harmonic Analysis, and Pseudo-Differential Operators on Lie Groups and Manifolds. Previously, he had appointments at Utrecht University, Johns Hopkins University, University of Edinburgh, and Imperial College London. He is the recipient of various awards and fellowships, notably, the Ferran Sunyer i Balaguer Prize in 2014 and 2018, Daiwa Adrian Prize in 2010, and the ISAAC award in 2007. He is serving as the head of the Ghent Analysis & PDE Center of Ghent University.