Convergence Of Fourier Series
In mathematics, the question of whether the Fourier series of a periodic function converges to the given function is researched by a field known as classical harmonic analysis, a branch of pure mathematics. Convergence is not necessarily a given in the general case, and there are criteria which need to be met in order for convergence to occur.
Determination of convergence requires the comprehension of pointwise convergence, uniform convergence, absolute convergence, Lp spaces, summability methods and the Cesàro mean.
Read more about Convergence Of Fourier Series: Preliminaries, Magnitude of Fourier Coefficients, Pointwise Convergence, Uniform Convergence, Absolute Convergence, Norm Convergence, Convergence Almost Everywhere, Summability, Order of Growth, Multiple Dimensions
Famous quotes containing the word series:
“I look on trade and every mechanical craft as education also. But let me discriminate what is precious herein. There is in each of these works an act of invention, an intellectual step, or short series of steps taken; that act or step is the spiritual act; all the rest is mere repetition of the same a thousand times.”
—Ralph Waldo Emerson (18031882)