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Unformatted text preview: on L 2 (0 , 2 ) so we know that it has a complete set oF eigenFunctions, e k , with eigenvalues k = 0 . rom the discussion above we then know that each e k is actually continuous since it is Aw with w L 2 (0 , 2 ) and hence also twice continuously dierentiable. So indeed, these e k satisFy the eigenvalue problem (with Dirichlet boundary conditions) with eigenvalues (22.3) T k = k 1 + c as k . The solvability part also Follows much the same way....
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This note was uploaded on 11/08/2011 for the course PHY 18.102 taught by Professor Staff during the Spring '09 term at MIT.
- Spring '09