最終更新日:2022/12/24
Indeed, if there is one property of locally compact groups more responsible than any other for the rich positive content of their representation theory, it is their possession of left-invariant and right-invariant (Haar) measures. The connection between the representation theory of a locally compact group and that of general Banach algebras proceeds directly from Lebesgue integration with respect to Haar measure on the group.
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Indeed,
if
there
is
one
property
of
locally
compact
groups
more
responsible
than
any
other
for
the
rich
positive
content
of
their
representation
theory,
it
is
their
possession
of
left-invariant
and
right-invariant
(Haar)
measures.
The
connection
between
the
representation
theory
of
a
locally
compact
group
and
that
of
general
Banach
algebras
proceeds
directly
from
Lebesgue
integration
with
respect
to
Haar
measure
on
the
group.