Metaplectic Groups and Segal Algebras
These notes give an account of recent work in harmonic analysis dealing with the analytical foundations of A. Weil's theory of metaplectic groups. It is shown that Weil's main theorem holds for a class of functions (a certain Segal algebra) larger than th
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1382 Hans Reiter
Metaplectic Groups and Segal Algebras
Springer-Verlag Berlin Heidelberg NewYork London Paris Tokyo Hong Kong
Author
Hans Reiter Institut fur Mathematik der Universitat Strudlhofgasse 4, 1090 Vienna, Austria
Mathematics Subject lJlaSSITlCatlOn usso): 4::lA'/U, 22LJ99, 11 R56 ISBN 3-540-51417-1 Springer-Verlag Berlin Heidelberg New York ISBN 0-387-51417-1 Springer-Verlag New York Berlin Heidelberg
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Herrn Professor Andre Weil in Verehrung und Dankbarkeit
This work originated in 1976 in an attempt to understand the proof, and the nature, moir
of the principal result,
'Sur certains
143211,
1964).
d o pe ra t e urs
groupes
But
the
t
scope
soon
theorem 6,
in A. Weil's me-
unitaires'
(Acta Math.
widened
when
it
that there is an intrinsic connexion between Weil's and a certain Segal algebra.
became
1l..1.
apparent
metaplectic group
Another task was to eliminate some diffi-
culties of an analytical nature in Weil's work, self in his Collected Papers (Springer,
1980),
hinted at by Weil himvol.
III,
p.445.
These notes may be considered as an addition to the author's book 'Classical Harmonic Analysis and Locally Compact Groups' versi ty Press, as a
rule,
1968).
full
Wei I' s
proofs are provided,
not been published before or differs, print.
(Oxford Uni-
theory is taken up at the beginning and. especially when the in some respect,
result
has
from those
in
Ample references to the literature are given to faci I i tate the
reader's task,
especially with regard to comparison.
Some new problems
that arise are pointed out. Some of the topics treated here were presented in seminars at University of Vienna
in
1978 and
in 1982,
but
since
then
the
the
whole
matter has undergone profound changes. A summary of the main results has appeared Acad.
Sci.
Paris,
Professor J. A short,
305 (1),
(Springer
241243
(1987),
in a
Note
in the C. R.
and I am grateful
to
Dieudonne for presenting it to the Academie des Sciences.
nontechnical
Proceedings
of LNM
cordially for Dr.
vol.
the
1359, the
survey
1987
of
some
Luxembourg
pp.238241).
invitation to
underlying
Symposium thank
the symposium.
Marc Burger for permission to
on
ideas
Professor I
is
Harmonic
in
the
Analysis
J. Po
also wish to
Pier thank
in
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