Displaying similar documents to “On a class of nonlocal elliptic operators for compact Lie groups. Uniformization and finiteness theorem”

On the index of nonlocal elliptic operators for compact Lie groups

Anton Savin (2011)

Open Mathematics

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We consider a class of nonlocal operators associated with a compact Lie group G acting on a smooth manifold. A notion of symbol of such operators is introduced and an index formula for elliptic elements is obtained. The symbol in this situation is an element of a noncommutative algebra (crossed product by G) and to obtain an index formula, we define the Chern character for this algebra in the framework of noncommutative geometry.

Solvability conditions for elliptic problems with non-Fredholm operators

V. Volpert, B. Kaźmierczak, M. Massot, Z. Peradzyński (2002)

Applicationes Mathematicae

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The paper is devoted to solvability conditions for linear elliptic problems with non-Fredholm operators. We show that the operator becomes normally solvable with a finite-dimensional kernel on properly chosen subspaces. In the particular case of a scalar equation we obtain necessary and sufficient solvability conditions. These results are used to apply the implicit function theorem for a nonlinear elliptic problem; we demonstrate the persistence of travelling wave solutions to spatially...