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The Convenient Setting of Global Analysis
 
Andreas Kriegl Universität Wien, Vienna, Austria
Peter W. Michor Universität Wien, Vienna, Austria
The Convenient Setting of Global Analysis
Hardcover ISBN:  978-0-8218-0780-4
Product Code:  SURV/53
List Price: $129.00
MAA Member Price: $116.10
AMS Member Price: $103.20
eBook ISBN:  978-0-8218-3396-4
Product Code:  SURV/53.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
Hardcover ISBN:  978-0-8218-0780-4
eBook: ISBN:  978-0-8218-3396-4
Product Code:  SURV/53.B
List Price: $254.00 $191.50
MAA Member Price: $228.60 $172.35
AMS Member Price: $203.20 $153.20
The Convenient Setting of Global Analysis
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The Convenient Setting of Global Analysis
Andreas Kriegl Universität Wien, Vienna, Austria
Peter W. Michor Universität Wien, Vienna, Austria
Hardcover ISBN:  978-0-8218-0780-4
Product Code:  SURV/53
List Price: $129.00
MAA Member Price: $116.10
AMS Member Price: $103.20
eBook ISBN:  978-0-8218-3396-4
Product Code:  SURV/53.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
Hardcover ISBN:  978-0-8218-0780-4
eBook ISBN:  978-0-8218-3396-4
Product Code:  SURV/53.B
List Price: $254.00 $191.50
MAA Member Price: $228.60 $172.35
AMS Member Price: $203.20 $153.20
  • Book Details
     
     
    Mathematical Surveys and Monographs
    Volume: 531997; 618 pp
    MSC: Primary 22; 26; 46; 58

    This book lays the foundations of differential calculus in infinite dimensions and discusses those applications in infinite dimensional differential geometry and global analysis not involving Sobolev completions and fixed point theory. The approach is simple: a mapping is called smooth if it maps smooth curves to smooth curves. Up to Fréchet spaces, this notion of smoothness coincides with all known reasonable concepts. In the same spirit, calculus of holomorphic mappings (including Hartogs' theorem and holomorphic uniform boundedness theorems) and calculus of real analytic mappings are developed. Existence of smooth partitions of unity, the foundations of manifold theory in infinite dimensions, the relation between tangent vectors and derivations, and differential forms are discussed thoroughly. Special emphasis is given to the notion of regular infinite dimensional Lie groups. Many applications of this theory are included: manifolds of smooth mappings, groups of diffeomorphisms, geodesics on spaces of Riemannian metrics, direct limit manifolds, perturbation theory of operators, and differentiability questions of infinite dimensional representations.

    Readership

    Graduate students and research mathematicians interested in global analysis and analysis on manifolds.

  • Table of Contents
     
     
    • Chapters
    • I. Calculus of smooth mappings
    • II. Calculus of holomorphic and real analytic mappings
    • III. Partitions of unity
    • IV. Smoothly realcompact spaces
    • V. Extensions and liftings of mappings
    • VI. Infinite dimensional manifolds
    • VII. Calculus on infinite dimensional manifolds
    • VIII. Infinite dimensional differential geometry
    • IX. Manifolds of mappings
    • X. Further applications
  • Reviews
     
     
    • Very interesting ... covers many topics that are difficult to find elsewhere in book form ... a valuable tool for self-study as well as an excellent reference.

      Mathematical Reviews
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 531997; 618 pp
MSC: Primary 22; 26; 46; 58

This book lays the foundations of differential calculus in infinite dimensions and discusses those applications in infinite dimensional differential geometry and global analysis not involving Sobolev completions and fixed point theory. The approach is simple: a mapping is called smooth if it maps smooth curves to smooth curves. Up to Fréchet spaces, this notion of smoothness coincides with all known reasonable concepts. In the same spirit, calculus of holomorphic mappings (including Hartogs' theorem and holomorphic uniform boundedness theorems) and calculus of real analytic mappings are developed. Existence of smooth partitions of unity, the foundations of manifold theory in infinite dimensions, the relation between tangent vectors and derivations, and differential forms are discussed thoroughly. Special emphasis is given to the notion of regular infinite dimensional Lie groups. Many applications of this theory are included: manifolds of smooth mappings, groups of diffeomorphisms, geodesics on spaces of Riemannian metrics, direct limit manifolds, perturbation theory of operators, and differentiability questions of infinite dimensional representations.

Readership

Graduate students and research mathematicians interested in global analysis and analysis on manifolds.

  • Chapters
  • I. Calculus of smooth mappings
  • II. Calculus of holomorphic and real analytic mappings
  • III. Partitions of unity
  • IV. Smoothly realcompact spaces
  • V. Extensions and liftings of mappings
  • VI. Infinite dimensional manifolds
  • VII. Calculus on infinite dimensional manifolds
  • VIII. Infinite dimensional differential geometry
  • IX. Manifolds of mappings
  • X. Further applications
  • Very interesting ... covers many topics that are difficult to find elsewhere in book form ... a valuable tool for self-study as well as an excellent reference.

    Mathematical Reviews
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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