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This four-part text beautifully interweaves theory and applications in Fuchsian Reduction. Background results in weighted Sobolev and Holder spaces as well as Nash-Moser implicit function theorem are provided. Most chapters contain a problem section and notes with references to the literature. This volume can be used as a text in graduate courses in PDEs and/or Algebra, or as a resource for researchers working with applications to Fuchsian Reduction. The comprehensive approach features the inclusion of problems and bibliographic notes.
From the reviews:
"Fuchsian reduction is an analytical method to represent solutions to non-linear PDEs near singularities ... . The book under review provides a careful and instructive introduction into this method. ... At the end of most of the chapters some problems are posed, which are solved in an appendix. In total this is a highly interesting book containing a lot of original ideas and which suggests new developments." (R. Steinbauer, Monatshefte für Mathematik, Vol. 158 (3), November, 2009)
"Fuchsian reduction is an analytical method to represent solutions to non-linear PDEs near singularities ... . The book under review provides a careful and instructive introduction into this method. ... At the end of most of the chapters some problems are posed, which are solved in an appendix. In total this is a highly interesting book containing a lot of original ideas and which suggests new developments." (R. Steinbauer, Monatshefte für Mathematik, Vol. 158 (3), November, 2009)