Mathematics and Its Applications

Geometric Theory of Generalized Functions with Applications to General Relativity

Authors: Grosser, M., Kunzinger, M., Oberguggenberger, M., Steinbauer, R.

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About this book

Over the past few years a certain shift of focus within the theory of algebras of generalized functions (in the sense of J. F. Colombeau) has taken place. Originating in infinite dimensional analysis and initially applied mainly to problems in nonlinear partial differential equations involving singularities, the theory has undergone a change both in in­ ternal structure and scope of applicability, due to a growing number of applications to questions of a more geometric nature. The present book is intended to provide an in-depth presentation of these develop­ ments comprising its structural aspects within the theory of generalized functions as well as a (selective but, as we hope, representative) set of applications. This main purpose of the book is accompanied by a number of sub­ ordinate goals which we were aiming at when arranging the material included here. First, despite the fact that by now several excellent mono­ graphs on Colombeau algebras are available, we have decided to give a self-contained introduction to the field in Chapter 1. Our motivation for this decision derives from two main features of our approach. On the one hand, in contrast to other treatments of the subject we base our intro­ duction to the field on the so-called special variant of the algebras, which makes many of the fundamental ideas of the field particularly transpar­ ent and at the same time facilitates and motivates the introduction of the more involved concepts treated later in the chapter.

Table of contents (5 chapters)

  • Colombeau’s Theory of Generalized Functions

    Grosser, Michael (et al.)

    Pages 1-100

  • Diffeomorphism Invariant Colombeau Theory

    Grosser, Michael (et al.)

    Pages 101-217

  • Generalized Functions on Manifolds

    Grosser, Michael (et al.)

    Pages 219-351

  • Applications to Lie Group Analysis of Differential Equations

    Grosser, Michael (et al.)

    Pages 353-414

  • Applications to General Relativity

    Grosser, Michael (et al.)

    Pages 415-472

Buy this book

eBook $79.99
price for USA (gross)
  • ISBN 978-94-015-9845-3
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $149.00
price for USA
  • ISBN 978-1-4020-0145-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $109.00
price for USA
  • ISBN 978-90-481-5880-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Geometric Theory of Generalized Functions with Applications to General Relativity
Authors
Series Title
Mathematics and Its Applications
Series Volume
537
Copyright
2001
Publisher
Springer Netherlands
Copyright Holder
Springer Science+Business Media Dordrecht
eBook ISBN
978-94-015-9845-3
DOI
10.1007/978-94-015-9845-3
Hardcover ISBN
978-1-4020-0145-1
Softcover ISBN
978-90-481-5880-5
Edition Number
1
Number of Pages
XV, 505
Topics