Geodesic
Boundary Value Problems with Non-Local Conditions
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 1 (2008) no. 2, pp. 158-187

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We describe a new algebra of boundary value problems which contains Lopatinskii elliptic as well as Toeplitz type conditions. These latter are necessary, if an analogue of the Atiyah–Bott obstruction does not vanish. Every elliptic operator is proved to admit up to a stabilisation elliptic conditions of such a kind. Corresponding boundary value problems are then Fredholm in adequate scales of spaces. The crucial novelty consists of the new type of weighted Sobolev spaces which fit well to the nature of pseudodifferential operators.
Keywords: pseudodifferential operators, boundary values problems, Toeplitz operators. 
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Nikolai N. Tarkhanov. Boundary Value Problems with Non-Local Conditions. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 1 (2008) no. 2, pp. 158-187. http://geodesic.mathdoc.fr/item/JSFU_2008_1_2_a5/