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An extension of the algebra of pseudodifferential operators, and some nonlocal elliptic problems. (English. Russian original) Zbl 0840.35132
Russ. Acad. Sci., Sb., Math. 81, No. 2, 363-396 (1995); translation from Mat. Sb. 185, No. 3, 117-159 (1994).
The authors study Fredholm properties for a certain class of elliptic problems. The operators corresponding to these problems form an algebra closed relative to adjoints, and are obtained as the elements of an extension of the set of pseudodifferential operators via a special class of nonlocal operators. These last operators are the Fourier integral operators associated with some fixed smooth bundle.

MSC:
35S15 Boundary value problems for PDEs with pseudodifferential operators
35J40 Boundary value problems for higher-order elliptic equations
47G30 Pseudodifferential operators
58J32 Boundary value problems on manifolds
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