Geodesic
On traces of operators associated with actions of compact Lie groups
Fundamentalʹnaâ i prikladnaâ matematika, Tome 21 (2016) no. 5, pp. 199-217 
A. Yu. Savin; B. Yu. Sternin. On traces of operators associated with actions of compact Lie groups. Fundamentalʹnaâ i prikladnaâ matematika, Tome 21 (2016) no. 5, pp. 199-217. http://geodesic.mathdoc.fr/item/FPM_2016_21_5_a9/
@article{FPM_2016_21_5_a9,
     author = {A. Yu. Savin and B. Yu. Sternin},
     title = {On traces of operators associated with actions of compact {Lie} groups},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {199--217},
     year = {2016},
     volume = {21},
     number = {5},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2016_21_5_a9/}
}
TY  - JOUR
AU  - A. Yu. Savin
AU  - B. Yu. Sternin
TI  - On traces of operators associated with actions of compact Lie groups
JO  - Fundamentalʹnaâ i prikladnaâ matematika
PY  - 2016
SP  - 199
EP  - 217
VL  - 21
IS  - 5
UR  - http://geodesic.mathdoc.fr/item/FPM_2016_21_5_a9/
LA  - ru
ID  - FPM_2016_21_5_a9
ER  - 
%0 Journal Article
%A A. Yu. Savin
%A B. Yu. Sternin
%T On traces of operators associated with actions of compact Lie groups
%J Fundamentalʹnaâ i prikladnaâ matematika
%D 2016
%P 199-217
%V 21
%N 5
%U http://geodesic.mathdoc.fr/item/FPM_2016_21_5_a9/
%G ru
%F FPM_2016_21_5_a9

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

Given a pair $(M,X)$, where $X$ is a smooth submanifold in a closed smooth manifold $M$, we study the operation that takes each operator $D$ on the ambient manifold to a certain operator on the submanifold. The latter operator is called the trace of $D$. More precisely, we study traces of operators associated with actions of compact Lie groups on $M$. We show that traces of such operators are localized at special submanifolds in $X$ and study the structure of the traces on these submanifolds.

[1] Loschenova D. A., “Zadachi Soboleva, assotsiirovannye s deistviyami grupp Li”, Differents. uravn., 51:8 (2015), 1056–1069 | DOI

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

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

[4] Savin A. Yu., Sternin B. Yu., “Nelokalnye ellipticheskie operatory dlya kompaktnykh grupp Li”, Dokl. RAN, 431:4 (2010), 457–460 | Zbl

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

[6] Savin A. Yu., Sternin B. Yu., “Ellipticheskie translyatory na mnogoobraziyakh s mnogomernymi osobennostyami”, Differents. uravn., 49:4 (2013), 513–527 | Zbl

[7] Sternin B. Yu., “Ellipticheskie i parabolicheskie zadachi na mnogoobraziyakh s granitsei, sostoyaschei iz komponent razlichnoi razmernosti”, Tr. MMO, 15, 1966, 346–382 | Zbl

[8] Khalmosh P., Sander V., Ogranichennye integralnye operatory v prostranstvakh $L^2$, Nauka, M., 1985 | MR

[9] Nazaikinskii V., Savin A., Schulze B.-W., Sternin B., Elliptic Theory on Singular Manifolds, CRC Press, Boca Raton, 2005 | MR

[10] Savin A. Yu., “On the index of nonlocal elliptic operators for compact Lie groups”, Central Eur. J. Math., 9:4 (2011), 833–850 | DOI | MR | Zbl

[11] Sternin B. Yu., “On a class of nonlocal elliptic operators for compact Lie groups. Uniformization and finiteness theorem”, Central Eur. J. Math., 9:4 (2011), 814–832 | DOI | MR | Zbl