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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.
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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