e start our consideration from the
Fourier
transform.
|
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(Direct Fourier transform)
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(Inverse Fourier transform)
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We aim to expand these relationships to a
transformation
where the
is a complex number
,
,
for some
.
The idea is to
split
and apply (
Direct Fourier
transform
),(
Inverse Fourier
transform
) to
.
Suppose the integral
converges absolutely for the given interval of values
.
We proceed according to the stated above idea:
We would like to recover the
from
.
We use (
Inverse Fourier transform
)
with the substitution
,
,
:
We transform the last
relationship:
Hence, we
invert
with
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