The term faltung is variously used to mean convolution and a function of bilinear forms.
Let and
be bilinear forms
(1)
| |||
(2)
|
and suppose that
and
are bounded in
with bounds
and
.
Then
(3)
|
where the series
(4)
|
is absolutely convergent, is called the faltung of and
.
is bounded in
, and its bound does not exceed
.