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Parametric Lie Group Actions on Global Generalised Solutions of Nonlinear Pdes : Including a Solution to Hilbert's Fifth Problem
by Elemer E. Rosinger


Overview - This book presents a solution of the harder part of the problem of defining globally arbitrary Lie group actions on such nonsmooth entities as generalised functions. Earlier, in part 3 of Oberguggenberger & Rosinger, Lie group actions were defined globally - in the projectable case - on the nowhere dense differential algebras of generalised functions An, as well as on the Colombeau algebras of generalised functions, and also on the spaces obtained through the order completion of smooth functions, spaces which contain the solutions of arbitrary continuous nonlinear PDEs.  Read more...

 
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More About Parametric Lie Group Actions on Global Generalised Solutions of Nonlinear Pdes by Elemer E. Rosinger
 
 
 
Overview
This book presents a solution of the harder part of the problem of defining globally arbitrary Lie group actions on such nonsmooth entities as generalised functions. Earlier, in part 3 of Oberguggenberger & Rosinger, Lie group actions were defined globally - in the projectable case - on the nowhere dense differential algebras of generalised functions An, as well as on the Colombeau algebras of generalised functions, and also on the spaces obtained through the order completion of smooth functions, spaces which contain the solutions of arbitrary continuous nonlinear PDEs. Further details can be found in Rosinger & Rudolph, and Rosinger & Walus 1,2]. To the extent that arbitrary Lie group actions are now defined on such nonsmooth entities as generalised functions, this result can be seen as giving an ans wer to Hilbert's fifth problem, when this problem is interpreted in its original full gener- ality, see for details chapter 11.


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Details
  • ISBN-13: 9780792352327
  • ISBN-10: 0792352327
  • Publisher: Springer
  • Publish Date: October 1998
  • Page Count: 238
  • Dimensions: 9.21 x 6.14 x 0.63 inches
  • Shipping Weight: 1.19 pounds

Series: Mathematics & Its Applications (Numbered Hardcover) #427

Related Categories

Books > Mathematics > Differential Equations - Partial
Books > Mathematics > Group Theory
Books > Mathematics > Mathematical Analysis

 
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