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Heat kernel asymptotics for roots of generalized Laplacians. (English) Zbl 1079.58020

Summary: We describe the heat kernel asymptotics for roots of a Laplace type operator \(\Delta\) on a closed manifold. A previously known relation between the Wodzicki residue of \(\Delta\) and heat trace asymptotics is shown to hold pointwise for the corresponding densities.

MSC:

58J40 Pseudodifferential and Fourier integral operators on manifolds
58J37 Perturbations of PDEs on manifolds; asymptotics
58J35 Heat and other parabolic equation methods for PDEs on manifolds
58J42 Noncommutative global analysis, noncommutative residues
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[1] DOI: 10.1016/S0393-0440(95)00061-5 · Zbl 0864.58057 · doi:10.1016/S0393-0440(95)00061-5
[2] Berline N., Heat Kernels and Dirac Operators (1991)
[3] DOI: 10.1016/S0550-3213(99)00590-8 · Zbl 0955.58021 · doi:10.1016/S0550-3213(99)00590-8
[4] DOI: 10.1090/S0002-9939-1990-1014642-X · doi:10.1090/S0002-9939-1990-1014642-X
[5] DOI: 10.1007/BF01418788 · Zbl 0281.35028 · doi:10.1007/BF01418788
[6] DOI: 10.1007/BF02506388 · Zbl 0881.58009 · doi:10.1007/BF02506388
[7] DOI: 10.1512/iumj.1985.34.34006 · Zbl 0571.53026 · doi:10.1512/iumj.1985.34.34006
[8] Gilkey P., Studies in Advanced Mathematics, in: Invariance Theory, the Heat Equation and the Atiyah–Singer Index Theorem (1995)
[9] DOI: 10.1080/03605309808821365 · Zbl 0911.35128 · doi:10.1080/03605309808821365
[10] DOI: 10.1063/1.531823 · Zbl 0877.58055 · doi:10.1063/1.531823
[11] DOI: 10.1006/jsco.1994.1018 · Zbl 0811.58057 · doi:10.1006/jsco.1994.1018
[12] DOI: 10.1016/0393-0440(94)00032-Y · Zbl 0826.58008 · doi:10.1016/0393-0440(94)00032-Y
[13] DOI: 10.1007/BF02099890 · Zbl 0823.58046 · doi:10.1007/BF02099890
[14] DOI: 10.4153/CJM-1949-021-5 · Zbl 0041.42701 · doi:10.4153/CJM-1949-021-5
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