This monograph provides some useful tools for performing global geometric analysis on real analytic manifolds. At the core of the methodology of the book is a variety of descriptions for the topologies for the space of real analytic sections of a real analytic vector bundle and for the space of real analytic mappings between real analytic manifolds. Among the various descriptions for these topologies is a development of geometric seminorms for the space of real analytic sections. To illustrate the techniques in the book, a number of fundamental constructions in differential geometry are shown to induce continuous mappings on spaces of real analytic sections and mappings.
Aimed at researchers at the level of Doctoral students and above, the book introduces the reader to the challenges and opportunities of real analytic analysis and geometry.
Notation and background.- Topology for spaces of real analytic sections and mappings.- Geometry: lifts and differentiation of tensors.- Analysis: norm estimates for derivatives.- Continuity of some standard geometric operations.
Prof. Andrew Lewis received his Doctorate in Applied Mechanics in 1995 from the California Institute of Technology. From 1996-1998 he was a Postdoctoral Fellow in the Mathematics Institute at the University of Warwick. In 1998, he joined the Department of Mathematics and Statistics at Queen's University, and has remained there till the present. He became Associate Professor in 2004 and Full Professor in 2014.He has published in the areas of geometric control theory, geometric mechanics, and geometric functional analysis. He has published three books: (1) Geometric Control of Mechanical Systems (with F. Bullo, Springer Texts in Applied Mathematics, 2004); (2) Time-Varying Vector Fields and Their Flows (with S. Jafarpoour, Springer Briefs in Mathematics, 2014); and (3) Tautological Control Systems (Springer Briefs in Control, 2014).
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