Consider the Sturm-Liouville system given by

ddx[p(x)dydx]+q(x)y+λr(x)y=0   axb (1)
a1y(a)+a2y(a)=0,b1y(b)+b2y(b)=0, (2)

where ai,bi with i{1,2} and p(x),q(x),r(x) are differentiable functions and λ. A non zero solution of the system defined by (1) and (2) exists in general for a specified λ. The functions corresponding to that specified λ are called eigenfunctions.

More generally, if D is some linear differential operator, and λ and f is a function such that Df=λf then we say f is an eigenfunction of D with eigenvalue λ.

Title eigenfunction
Canonical name Eigenfunction
Date of creation 2013-03-22 12:48:00
Last modified on 2013-03-22 12:48:00
Owner tensorking (373)
Last modified by tensorking (373)
Numerical id 8
Author tensorking (373)
Entry type Definition
Classification msc 34B24
Synonym characteristics functionMathworldPlanetmathPlanetmathPlanetmath
Defines solution of system