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 seriesMathworldPlanetmath of this function converges to f when f is continuousMathworldPlanetmath and to the arithmetic meanMathworldPlanetmath of the left-handed and right-handed http://planetmath.org/node/2950limit of f at a point where it is discontinuousMathworldPlanetmath.

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