Pseudo-differential operators and symmetries: background analysis and advanced topics

This monograph develops a global quantization theory of pseudo-differential operators on compact Lie groups. Traditionally, the theory of pseudo-differential operators was introduced in the Euclidean setting with the aim of tackling a number of important problems in analysis and in the theory of partial differential equations. This also yields a local theory of pseudo-differential operators on manifolds. The present book takes a different approach by using globalsymmetries of the space which are often available. First, a particular attention is paid to the theory of periodic operators, which are realized in the form of pseudo-differential and Fourier integral operators on the torus. Then, the cases of the unitary group SU(2) and the 3-sphere are analyzed in extensive detail. Finally, the monograph also develops elements of the theory of pseudo-differential operators on general compact Lie groups and homogeneous spaces. Provides an easy-to-read introduction to the theory of pseudo-differential operators and its more advanced aspects Contains a collection of necessary analytic tools which makes it excellent as a textbook on the subject Uniquely combines different parts of analysis and representation theory in a simple accessibleform. Usually these tools are scattered over different sources

• ISBN: 978-3-7643-8513-2
• Editorial: Birkhaüser
• Encuadernacion: Rústica
• Páginas: 400
• Fecha Publicación: 01/06/2009
• Nº Volúmenes: 1
• Idioma: Inglés