Noncommutative analysis


M. Ruzhansky, V. Turunen, Pseudo-Differential Operators and Symmetries, Birkhäuser, 2010. 724pp.
Link to publisher, Description and Samples, BookmetrixZB ReviewMR Review

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.

Poster_book Ruzhansky Turunen

Book-Fischer-Ruzhansky-cover-1V. Fischer, M. Ruzhansky, Quantization on Nilpotent Lie Groups, Progress in Math., Vol. 314, Birkhäuser, 2016. 557pp. BookmetrixZB Review, MR review

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.

Poster_book Fischer Ruzhansky

cover-ruzhansky-suragan-hardyM. 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

cwi-book-cover-centreRuzhansky, M. Regularity theory of Fourier integral operators with complex phases and singularities of affine fibrationsCWI 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 coefficientsMSJ Memoirs, 22, Mathematical Society of Japan, Tokyo, 2010. x+147pp. slightly older version at arxivsummary at World Scientific review

Cruz-Uribe D., Fiorenza A., Ruzhansky M., Wirth J., Variable Lebesgue Spaces and Hyperbolic SystemsAdvanced Courses in Mathematics – CRM Barcelona, Vol. 27, Birkhauser, 2014. Summary and link

Spectral geometry of partial differential operators


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

Poster_book Spectral_geometry

 Publications of Michael Ruzhansky can be found and downloaded here.

Thanks to Bolys Sabitbek for making the above book posters