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Geometric Analysis on Real Analytic Manifolds

  • Book
  • © 2023

Overview

Authors:
  1. Andrew D. Lewis

    1. Department of Mathematics and Statistics, Queens University, Kingston, Canada

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  • First comprehensive treatment of real analytic functional analysis with emphasis on differential geometry
  • Includes many separately interesting geometric techniques for geometric analysis on manifolds, for other regularity
  • With full detailed proofs and application of techniques to new results about continuity of geometric operations

Part of the book series: Lecture Notes in Mathematics (LNM, volume 2333)

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Table of contents (5 chapters)

  1. Front Matter

    Pages i-xv
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  2. Notation and Background

    • Andrew D. Lewis
    Pages 1-29

  3. Topology for Spaces of Real Analytic Sections and Mappings

    • Andrew D. Lewis
    Pages 31-92

  4. Geometry: Lifts and Differentiation of Tensors

    • Andrew D. Lewis
    Pages 93-199

  5. Analysis: Norm Estimates for Derivatives

    • Andrew D. Lewis
    Pages 201-251

  6. Continuity of Some Standard Geometric Operations

    • Andrew D. Lewis
    Pages 253-298

  7. Back Matter

    Pages 299-314
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Keywords

About this book

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.

Authors and Affiliations

  • Department of Mathematics and Statistics, Queens University, Kingston, Canada

    Andrew D. Lewis

About the author

​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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