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On the index of nonlocal elliptic operators associated with fibrations
No full text[No abstract available
Index of nonlocal elliptic operators over C*-algebras
No full textA study was conducted to demonstrate index of nonlocal elliptic operators over C*-algebras. The elliptic theory of pseudo-differential operators (PDOs) over C*-algebras was also constructed in the study. A nonlocal elliptic operator over C*-algebras associated with a discrete diffeomorphism group of a manifold was also considered for the study. A compact Lie group of diffeomorphisms of a compact closed connected manifold and a subgroup of polynomial growth were used in the study. The study provided a formula expressing the analytical numerical invariants of operators in topological terms. Using this formula a proof of higher index formula for nonlocal elliptic operators was derived
On the index of nonlocal elliptic operators associated with fibrations
No full text[No abstract available
Nonlocal elliptic operators for compact lie groups
No full textThe class of nonlocal operators corresponding to shifts along orbits under the action of a compact Lie group on a smooth manifold is considered. A Lie group invariant metric on the manifold and a normalized Haar measure corresponding to a bi-invariant metric on the group is assumed. It is found that the nonlocal operator is elliptic if there exists an element is invertible in the algebra. If a nonlocal operator is elliptic, then it is found to determine a Fredholm operator. For an orthonormal basic in the Lie algebra, the corresponding vector fields on the manifold are defined. An element is found to induce an orthogonal endomorphism of the bundle and the exterior form bundle. The restriction of operator to the subspace of sections invariant with respect to representation is isomorphic to the given nonlocal operator
On the index of elliptic operators for the group of dilations
No full textWe investigate nonlocal operators associated with the operators of compression and expansion. We obtain an ellipticity condition, which implies that the problem has the Fredholm property, compute the index, and study how the index depends on the exponent of the Sobolev space in which the problem is considered. © 2011 RAS(DoM) and LMS
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