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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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Principal symbol of a non-local operator and Atiyah–Singer index formula

I am trying to understand the Atiyah–Singer index formula for pseudo-differential operators. As far as I understood, the Fredholm index of the operator $A$ on a manifold can be computed just from the …
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