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Spectrum, resolvent, numerical range, functional calculus, operator semigroups. Special classes of operators: compact, Fredholm, dissipative, differential, integral, pseudodifferential, etc.

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Methods to find the spectrum of an operator

Suppose we have a bounded, self-adjoint operator $T$ on a set of functions $\mathcal{F}$. What kinds of methods are there to find the spectrum of $T$? Here is the setting I'm wondering about: consider …
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