Dirichlet conditions
Let f be a piecewise http://planetmath.org/node/1146regular real-valued function defined on some interval [a,b], such that f has only a finite number of discontinuities and extrema in [a,b]. Then the Fourier series of this function converges to f when f is continuous
and to the arithmetic mean
of the left-handed and right-handed http://planetmath.org/node/2950limit of f at a point where it is discontinuous
.
Title | Dirichlet conditions |
---|---|
Canonical name | DirichletConditions |
Date of creation | 2013-03-22 13:21:53 |
Last modified on | 2013-03-22 13:21:53 |
Owner | mathwizard (128) |
Last modified by | mathwizard (128) |
Numerical id | 6 |
Author | mathwizard (128) |
Entry type | Theorem |
Classification | msc 42A20 |
Related topic | FourierSeriesOfFunctionOfBoundedVariation |
Related topic | FourierCoefficients |