Remote access

How to Order

For AMS eBook frontlist subscriptions or backfile collection purchases:

   1a. To purchase any ebook backfile or to subscibe to the current year of Contemporary Mathematics, please download this required license agreement,

   1b. To subscribe to the current year of Memoirs of the AMS, please download this required license agreement.

   2. Complete and sign the license agreement.

   3. Email, fax, or send via postal mail to:

Customer Services
American Mathematical Society
201 Charles Street Providence, RI 02904-2294  USA
Phone: 1-800-321-4AMS (4267)
Fax: 1-401-455-4046

Visit the AMS Bookstore for individual volume purchases.

Browse the current eBook Collections price list

Powered by MathJax

On the foundations of nonlinear generalized functions I and II

About this Title

Michael Grosser, Eva Farkas, Michael Kunzinger and Roland Steinbauer

Publication: Memoirs of the American Mathematical Society
Publication Year 2001: Volume 153, Number 729
ISBNs: 978-0-8218-2729-1 (print); 978-1-4704-0322-5 (online)
MathSciNet review: 1848157
MSC: Primary 46F30; Secondary 26E15, 35A08, 35D05, 46G05, 46T30

View full volume PDF

Read more about this volume

View other years and numbers:

Table of Contents


  • Part 1. On the foundations of nonlinear generalized functions I
  • 1. Introduction
  • 2. Notation and terminology
  • 3. Scheme of construction
  • 4. Calculus
  • 5. C- and J-formalism
  • 6. Calculus on $U_\epsilon (\Omega )$
  • 7. Construction of a diffeomorphism invariant Colombeau algebra
  • 8. Sheaf properties
  • 9. Separating the basic definition from testing
  • 10. Characterization results
  • 11. Differential equations
  • Part 2. On the foundations of nonlinear generalized functions II
  • 12. Introduction to Part 2
  • 13. A simple condition equivalent to negligibility
  • 14. Some more calculus
  • 15. Non-injectivity of the canonical homomorphism from $\mathcal {G}^d(\Omega )$ into $\mathcal {G}^e(\Omega )$
  • 16. Classification of smooth Colombeau algebras between $\mathcal {G}^d(\Omega )$ and $\mathcal {G}^e(\Omega )$
  • 17. The algebra $\mathcal {G}^2$; classification results
  • 18. Concluding remarks