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