Let be L and G 2 linear operators so they have the same set of Eigenvalues, then:(adsbygoogle = window.adsbygoogle || []).push({});

[tex] L[y]=-\lambda _{n} y [/tex] and [tex] G[y]=-\lambda _{n} y [/tex]

then i believe that either L=G or L and G are related by some linear transform or whatever, in the same case it happens with Matrices having the same eigenvalues.

2. The second question is..if we have the Linear operator defining a PDE:

[tex] F(U_xx , U_yy , U_xy ,x,y)=0 [/tex]

Let's suppose we know the function U(x,y) that satisfy the PDE above, then what's the best method to solve:

[tex] F(U_xx , U_yy , U_xy ,x,y)=g(x,y) [/tex]

knowing the solution of the case where g(x,y)=0

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# A PDE and Linear operator questions.

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