On a class of pseudodifferential operators in $\mathbb R^m$ and on stratified manifolds
Sbornik. Mathematics, Tome 191 (2000) no. 5, pp. 725-757 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

A class of pseudodifferential operators in a subdomain of $\mathbb R^m$ that is well adapted to the transfer to manifolds with (intersecting) edges of various dimensions is considered. A version of symbolic calculus is discussed. The operators in question act in Sobolev spaces with weighted norms. Stratified manifolds (with edges as strata) are introduced and pseudodifferential operators on such manifolds are defined.
@article{SM_2000_191_5_a5,
     author = {B. A. Plamenevskii and V. N. Senichkin},
     title = {On a class of pseudodifferential operators in~$\mathbb R^m$ and on stratified manifolds},
     journal = {Sbornik. Mathematics},
     pages = {725--757},
     year = {2000},
     volume = {191},
     number = {5},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2000_191_5_a5/}
}
TY  - JOUR
AU  - B. A. Plamenevskii
AU  - V. N. Senichkin
TI  - On a class of pseudodifferential operators in $\mathbb R^m$ and on stratified manifolds
JO  - Sbornik. Mathematics
PY  - 2000
SP  - 725
EP  - 757
VL  - 191
IS  - 5
UR  - http://geodesic.mathdoc.fr/item/SM_2000_191_5_a5/
LA  - en
ID  - SM_2000_191_5_a5
ER  - 
%0 Journal Article
%A B. A. Plamenevskii
%A V. N. Senichkin
%T On a class of pseudodifferential operators in $\mathbb R^m$ and on stratified manifolds
%J Sbornik. Mathematics
%D 2000
%P 725-757
%V 191
%N 5
%U http://geodesic.mathdoc.fr/item/SM_2000_191_5_a5/
%G en
%F SM_2000_191_5_a5
B. A. Plamenevskii; V. N. Senichkin. On a class of pseudodifferential operators in $\mathbb R^m$ and on stratified manifolds. Sbornik. Mathematics, Tome 191 (2000) no. 5, pp. 725-757. http://geodesic.mathdoc.fr/item/SM_2000_191_5_a5/

[1] Dynin A. S., “Algebras generated by classical pseudodifferential operators on open Riemannian manifolds”, Proc. Sympos. Pure Math., 51:2 (1990), 93–98 | MR | Zbl

[2] Cordes H. O., Spectral theory of linear differential operators and comparison algebras, Cambridge Univ. Press, Cambridge, 1987 | MR | Zbl

[3] Melrose R. B., The Atiyah–Patodi–Singer index theorem, A. K. Peters, Wellesley, MA, 1994 | MR

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

[5] Schulze B.-W., Pseudo-differential operators on manifolds with singularities, North-Holland, Amsterdam, 1991 | MR | Zbl

[6] Mazya V. G., Plamenevskii B. A., “Ob odnom klasse mnogoobrazii s osobennostyami”, Izv. vuzov. Matematika, 1972, no. 11, 46–52 | Zbl

[7] Mazya V. G., Plamenevskii B. A., “Ellipticheskie kraevye zadachi na mnogoobraziyakh s osobennostyami”, Problemy matem. analiza, 1977, no. 6, 85–142 | Zbl

[8] Nazarov S. A., Plamenevskii B. A., Ellipticheskie zadachi v oblastyakh s kusochno gladkoi granitsei, Nauka, M., 1991

[9] Senichkin V. N., “Psevdodifferentsialnye operatory na mnogoobraziyakh s rebrami”, Problemy matem. analiza, 1992, no. 13, 162–214 | Zbl

[10] 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

[11] 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

[12] Plamenevskii B. A., Senichkin V. N., “Spektr algebry psevdodifferentsialnykh operatorov s kusochno gladkimi simvolami”, Izv. AN SSSR. Ser. matem., 53:1 (1989), 147–177 | MR

[13] Plamenevskii B. A., Senichkin V. N., “Razreshimye algebry operatorov”, Algebra i analiz, 6:5 (1994), 1–87 | MR

[14] Senichkin V. N., “Spektr algebry psevdodifferentsialnykh operatorov na mnogoobrazii s gladkimi rebrami”, Algebra i analiz, 8:6 (1996), 105–147 | MR

[15] Plamenevskii B. A., Senichkin V. N., “Psevdodifferentsialnye operatory na mnogoobraziyakh s osobennostyami”, Funkts. analiz i ego prilozh., 33:2 (1999), 88–90 | MR

[16] Agranovich M. S., Amosov B. A., “Otsenki $s$-chisel i spektralnye asimptotiki dlya integralnykh operatorov tipa potentsiala na negladkikh poverkhnostyakh”, Funkts. analiz i ego prilozh., 30:2 (1996), 1–18 | MR | Zbl

[17] Stein I., Singulyarnye integraly i differentsialnye svoistva funktsii, Mir, M., 1973 | MR

[18] Shubin M. A., Psevdodifferentsialnye operatory i spektralnaya teoriya, Nauka, M., 1978 | MR

[19] Khermander L., Analiz lineinykh differentsialnykh operatorov s chastnymi proizvodnymi, T. 3, Mir, M., 1987 | MR

[20] Plamenevskii B. A., Taschiyan G. M., “Operator svertki v prostranstvakh s vesom”, Problemy matem. analiza, 1990, no. 11, 208–237 | MR | Zbl