Some periodic functions can be described by Fourier series. For instance, for L2 functions, Carleson's theorem states that they have a pointwise (Lebesgue) almost everywhere convergent Fourier series. Fourier series can only be used for periodic functions, or for functions on a bounded (compact) interval. If is a periodic function with period that can be described by a Fourier series, the coefficients of the series can be described by an integral over an interval of length .
Some periodic functions can be described by Fourier series For instance for L2 functions Carleson's theorem states that they have a pointwise (Lebesgue) almost everywhere convergent Fourier series Fourier series can only be used for periodic functions or for functions on a bounded (compact) interval If is a periodic function with period that can be described by a Fourier series the coefficients of the series can be described by an integral over an interval of length 