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

Parametric Lie Group Actions on Global Generalised Solutions of Nonlinear Pdes: Including a Solution to Hilbert S Fifth Problem

Elemer E. Rosinger

Published October 31st 1998
ISBN : 9780792352327
Hardcover
238 pages
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 About the Book 

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 wereMoreThis 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 Hilberts fifth problem, when this problem is interpreted in its original full gener ality, see for details chapter 11.