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Clifford Algebras and Their Applications in Mathematical Physics, Vol. 2: Clifford Analysis

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In this second volume of the Proceedings of the Ixtapa Conference on Clifford Algebras and Their Applications to Mathematical Physics, the editors have collected papers which reflect the latest developments in Clifford Analysis. It is fair to say that the authors of the contributions are virtually all the important names in the field, and the picture that the volume presents of Clifford Analysis indicates the vitality of the topic. Maybe the most important thing in this volume (what I called the "new face" of Clifford Analysis) is the clear sense that Clifford Analysis is now used as a powerful tool to solve classical problems which the standards tools from the analysis in Euclidean spaces could not solve. This evolution from a discipline concerned with its own (quite interesting) internal problems, to a discipline capable of addressing outstanding issues in geometry and analysis is the product of the work of many of the contributors to these Proceedings. The volume is divided in four sections. The first deals with partial differential equations and boundary value problems. I particularly appreciated the survey work on the study of Beltrami type equations in three dimensions. The second section deals with Singular Integral Operators, the third offers some important Applications to Geometry and Physics, and the volume concludes with a section on Mobius Transformations and Monogenic Functions. I have found the papers of great interest because they not only address important and difficult problems, but also provide the reader with a wide variety of new issues to deal with. The majority of the papers is rather technical, and probably only accessible to the specialist, but a few of them (including the one on Beltrami equations I mentioned before) provide a sense of the state of the art, which is of great help to the analyst or the geometer who wishes to enter this beautiful branch of mathematics.