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Index of nonlocal problems associated with a bundle. (English. Russian original) Zbl 1310.47057
Differ. Equ. 50, No. 8, 1112-1121 (2014); translation from Differ. Uravn. 50, No. 8, 1118-1127 (2014).
In this paper, the authors consider an algebra of operators (already introduced in [the second author and V. E. Shalatov, Russ. Acad. Sci., Sb., Math. 81, No. 2, 363–396 (1995); translation from Mat. Sb. 185, No. 3, 117–159 (1994; Zbl 0840.35132)]) associated with a bundle, which contains, in particular, the algebra of pseudo-differential operators on the total space and also the operator of restriction and of integration along the fibers of the bundle. For the elements of this algebra the authors introduce the notion of ellipticity and for the elliptic elements they prove the Fredholm property and derive an index formula.
MSC:
47C05 Linear operators in algebras
47L80 Algebras of specific types of operators (Toeplitz, integral, pseudodifferential, etc.)
47G20 Integro-differential operators
58J22 Exotic index theories on manifolds
19K56 Index theory
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References:
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