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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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