41. In other words there is a Fourier series for " f " of the form 42. By strengthening the continuity assumption slightly one can easily show that the Fourier series converges everywhere. 43. Since floor and ceiling are not periodic, they do not have uniformly convergent Fourier series expansions. 44. The Fourier series exists and converges in similar ways to the [ ", ] case. 45. The spherical harmonic functions form a complete orthonormal set of functions in the sense of Fourier series . 46. Then the transform of the x [ n ] sequence has the form of a Fourier series . 47. After Salem's death his wife established an international prize for outstanding contributions to Fourier series . 48. In particular, if a function is continuously differentiable then its Fourier series converges to it everywhere. 49. FAST first represents conditional variances via coefficients from the multiple Fourier series expansion of the output function. 50. In 2011 she won the Salem Prize which is awarded for work associated with the Fourier Series .
