Geodesic
Schwartz Kernel Asymptotics and Regularized Traces of Diffusion Semigroups
Funkcionalʹnyj analiz i ego priloženiâ, Tome 44 (2010) no. 1, pp. 90-96.

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

The relationship between the parametrix of a diffusion type parabolic equation and the path integral representation of its fundamental solution provides an approach to computing the coefficients in the asymptotic expansion of the diffusion kernel constructively. The upper and lower bounds obtained in this paper for the regularized trace of the corresponding evolution semigroup strengthen and supplement the estimates which can be established by other methods.
Mots-clés : diffusion semigroup, Feynman–Kac formula.
Keywords: short-time asymptotics, regularized trace, parametrix 
@article{FAA_2010_44_1_a9,
     author = {S. A. Stepin},
     title = {Schwartz {Kernel} {Asymptotics} and {Regularized} {Traces} of {Diffusion} {Semigroups}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {90--96},
     publisher = {mathdoc},
     volume = {44},
     number = {1},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2010_44_1_a9/}
}
TY  - JOUR
AU  - S. A. Stepin
TI  - Schwartz Kernel Asymptotics and Regularized Traces of Diffusion Semigroups
JO  - Funkcionalʹnyj analiz i ego priloženiâ
PY  - 2010
SP  - 90
EP  - 96
VL  - 44
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/FAA_2010_44_1_a9/
LA  - ru
ID  - FAA_2010_44_1_a9
ER  - 
%0 Journal Article
%A S. A. Stepin
%T Schwartz Kernel Asymptotics and Regularized Traces of Diffusion Semigroups
%J Funkcionalʹnyj analiz i ego priloženiâ
%D 2010
%P 90-96
%V 44
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/FAA_2010_44_1_a9/
%G ru
%F FAA_2010_44_1_a9
S. A. Stepin. Schwartz Kernel Asymptotics and Regularized Traces of Diffusion Semigroups. Funkcionalʹnyj analiz i ego priloženiâ, Tome 44 (2010) no. 1, pp. 90-96. http://geodesic.mathdoc.fr/item/FAA_2010_44_1_a9/

[1] J. Hadamard, Lectures on Cauchy's Problem in Linear Partial Differential Equations, Dover Publ., New York, 1952 | MR | Zbl

[2] V. S. Buslaev, Problemy matem. fiz., 1966, no. 1, 82–101 | MR | Zbl

[3] S. Agmon, Y. Kannai, Israel J. Math., 5 (1967), 1–30 | DOI | MR | Zbl

[4] A. A. Arsenev, Zhurnal vych. matem. i matem. fiz., 7:6 (1967), 1298–1319 | MR

[5] V. S. Buslaev, Problemy matem. fiz., 1967, no. 2, 85–107 | MR | Zbl

[6] V. M. Babich, Yu. O. Rapoport, Problemy matem. fiz., 1974, no. 7, 21–38

[7] Y. Kannai, Commun. Partial Differ. Equations, 2:8 (1977), 781–830 | DOI | MR

[8] Y. Colin de Verdier, Ann. Sci. Ecole Norm. Sup. (4), 14:1 (1981), 27–39 | DOI | MR | Zbl

[9] D. R. Yafaev, Funkts. analiz i ego pril., 41:3 (2007), 60–83 | DOI | MR | Zbl

[10] V. A. Sadovnichii, V. E. Podolskii, UMN, 61:5 (2006), 89–156 | DOI | MR | Zbl

[11] B. Simon, Functional Integration and Quantum Physics, Academic Press, New York–London, 1979 | MR

[12] S. A. Molchanov, UMN, 30:1 (1975), 3–59 | MR | Zbl

[13] M. Hitrik, I. Polterovich, J. London Math. Soc., 68:2 (2003), 402–418 | DOI | MR | Zbl

[14] M. Sh. Birman, M. G. Krein, DAN SSSR, 144:3 (1962), 475–478 | MR | Zbl

[15] A. Sá Barreto, M. Zworski, Comm. Pure Appl. Math., 49 (1996), 1271–1280 | 3.0.CO;2-7 class='badge bg-secondary rounded-pill ref-badge extid-badge'>DOI | MR | Zbl

[16] E. Lieb, Bull. Amer. Math. Soc., 82:5 (1976), 751–753 | DOI | MR | Zbl

[17] M. Sh. Birman, V. A. Slousch, Funkts. analiz i ego pril., 43:3 (2009), 26–32 | DOI | MR