The Math Forum

Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Math Forum » Discussions » sci.math.* » sci.math

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

Topic: Eigenfunction question of a simple operator
Replies: 0  

Advanced Search

Back to Topic List Back to Topic List

Posts: 178
Registered: 11/9/07
Eigenfunction question of a simple operator
Posted: Nov 16, 2013 3:28 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply


Consider the integral operator defined via the following kernel k(x,y):

int_{-L}^L k(x,y)*f(y) dy = x^2*f(x)-c*f''(x)

where c>0 and L>0 are some given parameters. This operator is positive definite and self adjoint. So it must have some eigen decomposition.

Can any one help with computing the eigenfunctions and corresponding eigenvalues of this operator? I know eigenfunctions v_k(x) and eigenvalues a_k must satisfy:

forall x in [-L,L]: x^2*v_k(x)-c*v_k''(x)=a_k*v_k(x)

However, I have no clue how to find the solution of this simple equation.



Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© The Math Forum at NCTM 1994-2018. All Rights Reserved.