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@article{SEMR_2016_13_a51,
author = {V. A. Sharafutdinov},
title = {Application of geometric symbol calculus to computing heat invariants},
journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
pages = {491--524},
publisher = {mathdoc},
volume = {13},
year = {2016},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/SEMR_2016_13_a51/}
}
V. A. Sharafutdinov. Application of geometric symbol calculus to computing heat invariants. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 13 (2016), pp. 491-524. http://geodesic.mathdoc.fr/item/SEMR_2016_13_a51/
[1] I. G. Avramidi, “A covariant technique for the calculation of the one-loop effective action”, Nucl. Phys. B, 335 (1991), 712–754 | DOI | MR
[2] I. Avramidi, T. Branson, Heat kernel asymptotics of operators with non-Laplace principle part, Sep. 2001, arXiv: math-ph/9905001v2 | MR
[3] A. A. Belkov, A. V. Lanyov, A. Schalle, “Calculation of heat-kernel coefficients and usage of computer algebra”, Computer Physics Communications, 95:2–3 (1996), 123–130 | DOI | Zbl
[4] M. Berger, “Eigenvalues of the Laplacian”, Proc. Symp. in Pure Math., XVI, 1968, 121–126 | MR
[5] M. Berger, P. Gauduchon, E. Mazet, Le spectre d'une variété riemannienne, Lecture Notes in Math., 194, 1971 | DOI | Zbl
[6] N. Berline, E. Gertzer, M. Vergne, Heat kernels and Dirac operators, Grundlehren der Mathematischen Wissenschaften, 298, Springer, 1991
[7] I. Chavel, Eigenvalues in Riemannian Geometry, Academic Press, 1984 | MR | Zbl
[8] B. De Witt, Dynamical Theory of Groups and Fields, Gordon and Breach, New York, 1965 | MR
[9] V. V. Djepko, Yu. G. Nikonorov, “Double exponential map on spaces of constant curvature”, Siberian Advances Math., 10:1 (2007), 141–153 | MR | Zbl
[10] S. A. Fulling (ed.), Heat Kernel Techniques and Quantum Gravity, Discourses in Math. and its Appl., 4, Texas A Univ., 1995 | MR
[11] P. B. Gilkey, Invariance Theory, The Heat Equation, And the Atiyah-Singer Index Theorem, Publish or Parish, Inc. Wilmington, Delaware (U.S.A.), 1984 | MR | Zbl
[12] V. P. Gusynin, “Asymptotics of the heat kernel for nonmonimal operators”, Ukranian Math. Zh., 43 (1991), 1541–1551 | MR | Zbl
[13] V. P. Gusynin, V. V. Kornyak, “Complete computation of the De Witt–Seeley–Gilkey coefficent $E_4$ for nonmonimal operator on curved manifolds”, Fundamental and Applied Math., 5 (1999), 649–674 | MR | Zbl
[14] M. Kac, Can one hear the shape of a drum?, Amer. Math. Monthly, 73 (1966), 1–23 | DOI | MR | Zbl
[15] S. Minakshisundaram, “Eigenfunctions on Riemannian manifolds”, J. Indian Math. Soc. (N.S.), 17 (1953), 159–165 | MR
[16] V. K. Patodi, “Curvature and the fundamental solution of the heat operator”, J. Indian Math. Soc., 34 (1970), 269–285 | MR
[17] I. Polterovich, “Heat invariants of Riemannian manifolds”, Israel J. of Math., 119 (2000), 239–252 | DOI | MR | Zbl
[18] R. Seeley, “Complex powers of an elliptic operator”, Proc. Symp. Pure Math., 10, 1967, 288–307 | DOI | MR | Zbl
[19] V. Sharafutdinov, “Geometric symbol calculus for pseudodifferential operators I”, Siberian Advances Math., 15:3 (2005), 81–125 | MR | Zbl
[20] V. Sharafutdinov, “Geometric symbol calculus for pseudodifferential operators II”, Siberian Advances Math., 15:4 (2005), 71–95 | MR | Zbl
[21] V. Sharafutdinov, Supplements to “Geometric symbol calculus for pseudodifferential operators”, Preprint, , 2002 http://www.math.nsc.ru/s̃harafutdinov/publications
[22] M. Skokan, Rho's, Unpublished notes, 2003
[23] C. Xu, “Heat kernels and geometric invariants I”, Bull. Sc. Math., 117:2 (1993), 287–312 | MR | Zbl