Nonlocal Elliptic Operators
Just as in the case of usual local elliptic (pseudo)differential operators, the theory of nonlocal elliptic operators is based on the scalar case, i.e., the case of operators acting in spaces of functions. Indeed, a majority of typical facts and situations of the theory (including the issues related to the finiteness theorem) fully manifest themselves already in this case. After the theory has been developed for scalar operators, the generalization of the definitions and theorems to the case of operators acting in spaces of sections of arbitrary bundles on the manifold M is a nearly (though not 100%) standard exercise. Thus, we start from scalar operators.
KeywordsOrder Zero Scalar Operator Zero Section Fredholm Property Ellipticity Condition
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