Geodesic
On Traces of Fourier Integral Operators on Submanifolds
Matematičeskie zametki, Tome 104 (2018) no. 4, pp. 588-603.

Voir la notice de l'article provenant de la source Math-Net.Ru

Given a smooth embedding of manifolds and a Fourier integral operator on the ambient manifold, the trace of this operator on the submanifold (i.e., its composition with the boundary and coboundary operators, which is an operator on the submanifold) is considered. Conditions under which such a trace is also a Fourier integral operator are determined, and its amplitude in canonical local coordinates is calculated. The results are applied to quantized canonical transformations.
Keywords: Fourier integral operators, traces of operators on submanifolds, relative elliptic theory, trace of a Lagrangian manifold.
Mots-clés : quantized canonical transformations 
@article{MZM_2018_104_4_a7,
     author = {P. A. Sipailo},
     title = {On {Traces} of {Fourier} {Integral} {Operators} on {Submanifolds}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {588--603},
     publisher = {mathdoc},
     volume = {104},
     number = {4},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2018_104_4_a7/}
}
TY  - JOUR
AU  - P. A. Sipailo
TI  - On Traces of Fourier Integral Operators on Submanifolds
JO  - Matematičeskie zametki
PY  - 2018
SP  - 588
EP  - 603
VL  - 104
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2018_104_4_a7/
LA  - ru
ID  - MZM_2018_104_4_a7
ER  - 
%0 Journal Article
%A P. A. Sipailo
%T On Traces of Fourier Integral Operators on Submanifolds
%J Matematičeskie zametki
%D 2018
%P 588-603
%V 104
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2018_104_4_a7/
%G ru
%F MZM_2018_104_4_a7
P. A. Sipailo. On Traces of Fourier Integral Operators on Submanifolds. Matematičeskie zametki, Tome 104 (2018) no. 4, pp. 588-603. http://geodesic.mathdoc.fr/item/MZM_2018_104_4_a7/

[1] S. P. Novikov, B. Yu. Sternin, “Sledy ellipticheskikh operatorov na podmnogoobraziyakh i $K$-teoriya”, Dokl. AN SSSR, 170:6 (1966), 1265–1268 | MR | Zbl

[2] S. P. Novikov, B. Yu. Sternin, “Ellipticheskie operatory i podmnogoobraziya”, Dokl. AN SSSR, 171:3 (1966), 525–528 | MR | Zbl

[3] B. Yu. Sternin, “Otnositelnaya ellipticheskaya teoriya i problema S. L. Soboleva”, Dokl. AN SSSR, 230:2 (1976), 287–290 | MR | Zbl

[4] V. Nazaikinskii, B. Sternin, “Relative elliptic theory”, Aspects of Boundary Problems in Analysis and Geometry, Oper. Theory Adv. Appl., 151, Birkhäuser, Basel, 2004, 495–560 | MR

[5] B. Yu. Sternin, “Ellipticheskie i parabolicheskie zadachi na mnogoobraziyakh s granitsei, sostoyaschei iz komponent razlichnoi razmernosti”, Tr. MMO, 15, Izd-vo Mosk. un-ta, M., 1966, 346–382 | MR | Zbl

[6] B. Yu. Sternin, V. E. Shatalov, “Otnositelnaya ellipticheskaya teoriya i zadacha Soboleva”, Matem. sb., 187:11 (1996), 115–144 | DOI | MR | Zbl

[7] A. Yu. Savin, B. Yu. Sternin, “O nelokalnykh zadachakh Soboleva”, Dokl. AN, 451:3 (2013), 259–263 | DOI | MR | Zbl

[8] A. Yu. Savin, B. Yu. Sternin, “Ellipticheskie translyatory na mnogoobraziyakh s tochechnymi osobennostyami”, Differents. uravneniya, 48:12 (2012), 1612–1620 | MR | Zbl

[9] A. Yu. Savin, B. Yu. Sternin, E. Shroe, “Ellipticheskie operatory, assotsiirovannye s gruppami kvantovannykh kanonicheskikh preobrazovanii”, UMN, 73:3 (441) (2018), 179–180 | DOI

[10] P. A. Sipailo, “Sledy kvantovannykh kanonicheskikh preobrazovanii, sosredotochennye na konechnom mnozhestve tochek”, Differents. uravneniya, 54:5 (2018), 701–712 | DOI

[11] L. Khermander, Analiz lineinykh differentsialrykh operatorov s chastnymi proizvodnymi. T. 3. Psevdodifferentsialnye operatory, Mir, M., 1987 | MR

[12] L. Khermander, Analiz lineinykh differentsialrykh operatorov s chastnymi proizvodnymi. T. 4. Integralnye operatory Fure, Mir, M., 1988 | MR

[13] F. Trev, Vvedenie v teoriyu psevdodifferentsialnykh operatorov i integralnykh operatorov Fure, T. 2, Mir, M., 1984 | MR

[14] V. P. Maslov, Teoriya vozmuschenii i asimptoticheskie metody, Izd-vo Mosk. un-ta, M., 1965

[15] V. E. Nazaikinskii, V. G. Oshmyan, B. Yu. Sternin, V. E. Shatalov, “Integralnye operatory Fure i kanonicheskii operator”, UMN, 36:2 (218) (1981), 81–140 | MR | Zbl

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