Magnitude of Fourier Coefficients
In applications, it is often useful to know the size of the Fourier coefficient.
If is an absolutely continuous function,
for a constant that only depends on .
If is a bounded variation function,
If
If and has modulus of continuity,
and therefore, if is in the α-Hölder class
Read more about this topic: Convergence Of Fourier Series
Famous quotes containing the words magnitude of and/or magnitude:
“Sometimes you’re overwhelmed when a thing comes, and you do not realize the magnitude of the affair at that moment. When you get away from it, you wonder, did it really happen to you.”
—Marian Anderson (1902–1993)
“My time has come.
There are twenty people in my belly,
there is a magnitude of wings,
there are forty eyes shooting like arrows,
and they will all be born.
All be born in the yellow wind.”
—Anne Sexton (1928–1974)