Editing Discrete Laplace operator (section)

==Spectrum==
The spectrum of the discrete Laplacian on an infinite grid is of key interest; since it is a [[self-adjoint operator]], it has a real spectrum. For the convention <math>\Delta = I - M</math> on <math>Z</math>, the spectrum lies within <math>[0,2]</math> (as the averaging operator has spectral values in <math>[-1,1]</math>). This may also be seen by applying the Fourier transform. Note that the discrete Laplacian on an infinite grid has purely absolutely continuous spectrum, and therefore, no eigenvalues or eigenfunctions.