The above result, commonly known as the Riemann-Lebesgue lemma, is of basic importance in harmonic analysis. It is equivalent to the assertion that the Fourier coefficients of a periodic, integrable function , tend to as .
The proof can be organized into 3 steps.
Step 1. An elementary calculation shows that
Step 3. Let be an arbitrary measurable function, integrable on . The proposition is true for such a general , because one can always write
where and are positive functions, integrable on .
|Date of creation||2013-03-22 13:08:04|
|Last modified on||2013-03-22 13:08:04|
|Last modified by||rmilson (146)|