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Elliptic dilation-contraction problems on manifolds with boundary. \(C^*\)-theory. (English. Russian original) Zbl 06695400
Differ. Equ. 52, No. 10, 1331-1340 (2016); translation from Differ. Uravn. 52, No. 10, 1383-1392 (2016).
Summary: We study boundary value problems with dilations and contractions on manifolds with boundary. We construct a \(C^*\)-algebra of such problems generated by zero-order operators. We compute the trajectory symbols of elements of this algebra, obtain an analog of the Shapiro-Lopatinskii condition for such problems, and prove the corresponding finiteness theorem.

MSC:
47C15 Linear operators in \(C^*\)- or von Neumann algebras
35 Partial differential equations
46L Selfadjoint operator algebras (\(C^*\)-algebras, von Neumann (\(W^*\)-) algebras, etc.)
58J40 Pseudodifferential and Fourier integral operators on manifolds
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