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5. Spectral theory and separation of variables
For many of the partial differential equations discussed above, it's the separation-of-variables method (consisting of searching for possible solutions of the form :
and then to form linear combinations of them, possibly infinite in some sense to be specified) which has often made it possible to determine the sought-after solutions.
The theoretical (and also practical for many simple special cases) success of this method rests on the foundations we now set...
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Spectral theory and separation of variables
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