Pseudo-Differential Operators and Symmetries

From the reviews: "This book presents recent results on the global theory of pseudo-differential operators on compact Lie groups along with a bulk of background material. ... this very welcomed book is a profitable read for specialists and-due to the included background material, which makes it self-contained-also for graduate students." (R. Steinbauer, Monatshefte fur Mathematik, 2013) "The present book is devoted to the theory of pseudodifferential operators on spaces with symmetries ... . Summing up, this welcome book is nicely written and looks very appealing for researchers in the fields of Euclidean and abstract harmonic analysis and pseudodifferential operators, as well as for any Ph.D. student interested in those topics." (Fabio Nicola, Mathematical Reviews, Issue 2011 b) "The book is devoted to a global theory of pseudo-differential operators on compact Lie groups. ... In the whole, including background material and new results about operators on Lie groups, the book offers a pleasant and profitable reading to graduate students and specialists." (Luigi Rodino, Zentralblatt MATH, Vol. 1193, 2010)

• Foundations of Analysis.- Sets, Topology and Metrics.- Elementary Functional Analysis.- Measure Theory and Integration.- Algebras.- Commutative Symmetries.- Fourier Analysis on ?n.- Pseudo-differential Operators on ?n.- Periodic and Discrete Analysis.- Pseudo-differential Operators on .- Commutator Characterisation of Pseudo-differential Operators.- Representation Theory of Compact Groups.- Groups.- Topological Groups.- Linear Lie Groups.- Hopf Algebras.- Non-commutative Symmetries.- Pseudo-differential Operators on Compact Lie Groups.- Fourier Analysis on SU(2).- Pseudo-differential Operators on SU(2).- Pseudo-differential Operators on Homogeneous Spaces.