科研之友
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摘要
We define classes of pseudodifferential operators on G-bundles with compact base and give a generalized L (2) Fredholm theory for invariant operators in these classes in terms of von Neumann%26apos;s G-dimension. We combine this formalism with a generalized Paley-Wiener theorem, valid for bundles with unimodular structure groups, to provide solvability criteria for invariant operators. This formalism also gives a basis for a G-index for these operators. We also define and describe a transversal dimension and its corresponding Fredholm theory in terms of anisotropic Sobolev estimates, valid also for similar bundles with nonunimodular structure group.
- 出版日期2013-4
