In this book the global analysis of pseudo-differential operators is consistently developed in the setting of compact Lie groups. The book also contains the background material on related topics of analysis, and is related to time-frequency analysis. Some extracts from the book can be downloaded here.
This book is the winner of the Ferran Sunyer I Balaguer Prize 2014
In this book the global quantization constructions of the previous work have been developed in the setting of general graded Lie groups. There is also an extensive presentation of the background analysis on stratified, graded, and general homogeneous groups. This book is open access and can be downloaded here.
M. Ruzhansky, D. Suragan, Hardy inequalities on homogeneous groups (100 Years of Hardy Inequalities), Progress in Math., Vol. 327, Birkhäuser, 2019.573 pp.
This book is the winner of the Ferran Sunyer i Balaguer Prize 2018
This open access book provides an extensive treatment of Hardy inequalities and closely related topics from the point of view of Folland and Stein’s homogeneous (Lie) groups.
Fourier integral operators
Ruzhansky, M. Regularity theory of Fourier integral operators with complex phases and singularities of affine fibrations, CWI Tracts, vol. 131, 2001. Stichting Mathematisch Centrum, Centrum voor Wiskunde en Informatica, Amsterdam, 2001. vi+130 pp. download review Contents and introduction
Hyperbolic Partial Differential Equations
Ruzhansky M., Smith J., Dispersive and Strichartz estimates for hyperbolic equations with constant coefficients, MSJ Memoirs, 22, Mathematical Society of Japan, Tokyo, 2010. x+147pp. slightly older version at arxiv; summary at World Scientific review
Cruz-Uribe D., Fiorenza A., Ruzhansky M., Wirth J., Variable Lebesgue Spaces and Hyperbolic Systems, Advanced Courses in Mathematics – CRM Barcelona, Vol. 27, Birkhauser, 2014. Summary and link
In the last couple of years we have been also doing research on isoperimetric inequalities for integral operators of different types. This research together with some other things, and the extensive introductory background notes on the relevant spectral theory appeared in:
M. Ruzhansky, M. Sadybekov, D. Suragan, Spectral geometry of partial differential operators, Monographs and Research Notes in Mathematics, Chapman and Hall/CRC Press, 2020. 366pp. link
⛹ Publications of Michael Ruzhansky can be found and downloaded here.