Last Updated：2022/12/24
There is a large and important literature concerned with the question of how to characterize precisely the boundary values of analytic functions. For example, when the analytic functions are of Hardy Class H* in a half plane, then their boundary values are attained in the L2 norm and, in fact, the analytic function can be reproduced by a Cauchy integral of the boundary value.
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There
is
a
large
and
important
literature
concerned
with
the
question
of
how
to
characterize
precisely
the
boundary
values
of
analytic
functions.
For
example,
when
the
analytic
functions
are
of
Hardy
Class
H^*
in
a
half
plane,
then
their
boundary
values
are
attained
in
the
L2
norm
and,
in
fact,
the
analytic
function
can
be
reproduced
by
a
Cauchy
integral
of
the
boundary
value.
