hat happens if one takes Fourier series
of non-periodic function? To put the question in exact terms, suppose the
function
is such that the restriction of it to the interval
belongs to
.
We form the
function
with the functions
being the Fourier exponentials normalized to
.
Such function will be the
-periodic
repetition of the restriction
to the intervals
,
:
This is so because the function
is
-periodic
and the sum
is the Fourier series of
.
Then by uniqueness of Fourier series for
-periodic
functions we must
have
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