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

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