Preface to the English
We are happy to welcome the English translation of our book, which origi-
nally appeared under the title 'Operateurs pseudo-differentiels et theoreme
de Nash-Moser' in 1991 (InterEditions/Editions du CNRS, Paris).
Though the world of partial differential equations has changed a lot
during these years, we think that the elementary presentation of the subjects
touched upon in our book is still up to date and can be useful; thus, we
made no changes, except for correcting some misprints. On the other hand,
several remarkable books on partial differential equations have appeared
since: though their scopes largely exceed that of our book, we thought it
relevant to mention them in our bibliography.
Finally, we wish to thank the translator, Dr. Stephen S. Wilson, and the
editorial board of the AMS, who worked to produce this new edition of our
Orsay, November 2006 Serge Alinhac and Patrick Gerard
The numbering system I have used in my translation is essentially that employed
by the authors in the original French edition so that the actual equation numbers
etc. are the same in both versions. I did, however, make certain changes to the
cross-referencing system: for example, to remove ambiguity, outside of Chapter II
Exercise A.l of that chapter may be referred to here as Exercise II.A. 1 although
within Chapter II it is referred to as Exercise A.l.
Cheltenham, February 2007 Stephen S. Wilson