Geodesic
On the algebra of operators corresponding to the union of smooth submanifolds
Contemporary Mathematics. Fundamental Directions, Proceedings of the S.M. Nikolskii Mathematical Institute of RUDN University, Tome 65 (2019) no. 4, pp. 672-682.

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For a pair of smooth transversally intersecting submanifolds in some enveloping smooth manifold, we study the algebra generated by pseudodifferential operators and (co)boundary operators corresponding to submanifolds. We establish that such an algebra has 18 types of generating elements. For operators from this algebra, we define the concept of symbol and obtain the composition formula. 
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D. A. Poluektova; A. Yu. Savin; B. Yu. Sternin. On the algebra of operators corresponding to the union of smooth submanifolds. Contemporary Mathematics. Fundamental Directions, Proceedings of the S.M. Nikolskii Mathematical Institute of RUDN University, Tome 65 (2019) no. 4, pp. 672-682. http://geodesic.mathdoc.fr/item/CMFD_2019_65_4_a8/

[1] M. I. Zelikin, B. Yu. Sternin, “On one system of integral equations arising in the Sobolev problem”, Siberian Math. J., 18:1 (1977), 97–102 (in Russian) | MR | Zbl

[2] D. A. Loshchenova, “Sobolev problems associated with actions of Lie groups”, Differ. Equ., 51:8 (2015), 1056–1069 (in Russian) | DOI

[3] V. E. Nazaykinskiy, B. Yu. Sternin, “On the Green operator in the relative elliptic theory”, Rep. Russ. Acad. Sci., 391:3 (2003), 306–309 (in Russian) | MR | Zbl

[4] L. L. Nguyen, “On nonlocal Sobolev problems”, Differ. Equ., 48:8 (2012), 1192–1196 (in Russian) | MR

[5] S. P. Novikov, B. Yu. Sternin, “Traces of elliptic operators on submanifolds and the $K$-theory”, Rep. Acad. Sci. USSR, 170:6 (1966), 1265–1268 (in Russian) | Zbl

[6] A. Yu. Savin, B. Yu. Sternin, “Elliptic translators on manifolds with multidimensional singularities”, Differ. Equ., 49:4 (2013), 513–527 (in Russian) | Zbl

[7] A. Yu. Savin, B. Yu. Sternin, “The index of Sobolev problems on manifolds with multidimensional singularities”, Differ. Equ., 50:2 (2014), 229–241 (in Russian) | DOI | Zbl

[8] B. Yu. Sternin, “Elliptic and parabolic problems on manifolds with the boundary consisting of components of different dimension”, Proc. Moscow Math. Soc., 15, 1966, 346–382 (in Russian) | Zbl

[9] B. Yu. Sternin, “Elliptic (co)boundary morphisms”, Rep. Acad. Sci. USSR, 172:1 (1967), 44–47 (in Russian) | Zbl

[10] B. Yu. Sternin, “Elliptic morphisms on manifolds with singularities (rigging of an elliptic operator)”, Rep. Acad. Sci. USSR, 200:1 (1971), 45–48 (in Russian) | Zbl

[11] B. Yu. Sternin, V. E. Shatalov, “Relative elliptic theory and the Sobolev problem”, Math. Digest, 187:11 (1996), 115–144 (in Russian) | DOI | MR | Zbl

[12] L. Hörmander, “Pseudo-differential operators”, Commun. Pure Appl. Math., 18 (1965), 501–517 | DOI | MR | Zbl

[13] V. Nazaikinskii, B. Sternin, “Relative elliptic theory”, Aspects of Boundary Problems in Analysis and Geometry, Birkhäuser, Basel—Boston—Berlin, 2004, 495–560 | DOI | MR | Zbl

[14] S. Rempel, B. W. Schulze, Index theory of elliptic boundary problems, Akademie-Verlag, Berlin, 1982 | MR | Zbl