Geodesic
The spectrum of an algebra of pseudodifferential operators with piecewise smooth symbols
Izvestiya. Mathematics , Tome 34 (1990) no. 1, pp. 147-179.

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The authors study the spectrum of a $C^*$-algebra of pseudodifferential operators whose symbols have discontinuities along submanifolds (the supports of the discontinuities) intersecting at nonzero angles. All (up to equivalence) irreducible representations of such algebras are enumerated, a realization of these representations is indicated, and the spectral topology is described. Bibliography: 7 titles. 
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B. A. Plamenevskii; V. N. Senichkin. The spectrum of an algebra of pseudodifferential operators with piecewise smooth symbols. Izvestiya. Mathematics , Tome 34 (1990) no. 1, pp. 147-179. http://geodesic.mathdoc.fr/item/IM2_1990_34_1_a6/

[1] Plamenevskii B. A., Senichkin V. N., “O spektre $C^*$-algebr, porozhdennykh psevdodifferentsialnymi operatorami s razryvnymi simvolami”, Izv. AN SSSR. Ser. matem., 47:6 (1983), 1263–1284 | MR | Zbl

[2] Plamenevskii B. A., Algebry psevdodifferentsialnykh operatorov, Nauka, M., 1986 | MR

[3] Plamenevskii B. A., Senichkin V. P., “O spektre $C^*$-algebr psevdodifferentsialnykh operatorov s mnogomernymi osobennostyami v simvolakh”, Funkts. analiz i ego prilozh., 20:4 (1986), 85–86 | MR | Zbl

[4] Plamenevskii B. A., Senichkin V. N., “O predstavleniyakh algebry psevdodifferentsialnykh operatorov s mnogomernymi razryvami v simvolakh”, Izv. AN SSSR. Ser. matem., 51:4 (1987), 833–859 | MR

[5] Plamenevskii B. A. Senichkin V. N., “Predstavleniya $C^*$-algebr, porozhdennykh psevdodifferentsialnymi operatorami v prostranstvakh s vesom”, Problemy matem. fiziki, 1987, no. 12, 165–189, LGU | MR

[6] Plamenevskii B. A., Senichkin V. N., “Algebry psevdodifferentsialnykh operatorov s kusochno gladkimi simvolami”, Dokl. AN SSSR, 298:1 (1988), 40–44 | MR | Zbl

[7] Diksme Zh., $C^*$-algebry i ikh predstavleniya, Nauka, M., 1974 | MR