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Unformatted text preview: tion of a vibrating string) ( T ( x ) y ( x )) + ( x ) y ( x ) = 0 , x [0 ,L ] , where T ( x ) , ( x ) > with boundary conditions y (0) = 0 , my ( L ) + k y ( L ) = 0 (the endpoint x = 0 is kept xed, and the other end, x = L is accelerated up and down with no transversal force). Reformulate this problem using a self-adjoint dierential operator on an appropriate Hilbert space: give the operator, its domain, and show that it is self-adjoint. Is this operator positive denite? Without explicitly solving the problems, what can you say about the eigenvalues and eigenfunctions of this problem? 1...
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- Spring '12