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Heat Content Asymptotics for Operators of Laplace Type with Spectral Boundary Conditions

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Abstract

Let P be an operator of Dirac type and let D=P 2 be the associated operator of Laplace type. We impose spectral boundary conditions and study the leading heat content coefficients for D.

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References

  1. Atiyah, M. F., Patodi, V. K., and Singer, I. M.: Spectral asymmetry and Riemannian geometry, Math. Proc. Cambridge Philos. Soc. I, 77 (1975), 43–69; II, 78 (1975), 405-432; III, 79 (1976), 71-99.

    Google Scholar 

  2. Van den Berg, M., Desjardins, S., and Gilkey, P. B.: Functorality and heat content asymptotics for operators of Laplace type, Topol. Methods Nonlinear Anal. 2 (1993), 147–162.

    Google Scholar 

  3. Van den Berg, M., and Gilkey, P. B.: Heat content asymptotics of a Riemannian manifold with boundary, J. Funct. Anal. 120 (1994), 48–71.

    Google Scholar 

  4. Desjardins, S., and Gilkey, P. B.: Heat content asymptotics for operators of Laplace type with Neumann boundary conditions, Math. Z. 215 (1994), 251–268.

    Google Scholar 

  5. Dowker, J. S., Gilkey, P. B., and Kirsten, K.: Heat asymptotics with spectral boundary conditions, Contemp. Math. 242 (1999), 107–124. hep-th/0004020.

    Google Scholar 

  6. Gilkey, P.: On the index of geometrical operators on Riemannian manifolds with boundary, Adv. Math. 102 (1993), 129–183.

    Google Scholar 

  7. Gilkey, P. B., and Kirsten, K.: Heat asymptotics with spectral boundary conditions II, Proc. Roy. Soc. Edinburgh A 133 (2003), 333–361. math-ph/0007015.

    Google Scholar 

  8. Gilkey, P. B., Kirsten, K., and Park, J. H.: Heat content asymptotics for oblique boundary conditions, Lett. Math. Phys. 59 (2002), 269–276.

    Google Scholar 

  9. Gilkey, P. B., Kirsten, K., and Park, J. H.: Heat content asymptotics for spectral boundary conditions, In: Trends Math. 5 (2002), 49–58. math-ph/0209012.

    Google Scholar 

  10. Grubb, G.: Heat operator trace expansions and index for general Atiyah-Patodi-Singer boundary problems, Comm. Partial Differential Equations 17 (1992), 2031–2077.

    Google Scholar 

  11. Grubb, G.: Trace expansions for pseudo Differential boundary problems for Dirac operators and more general systems, Ark. Math. 37 (1999), 45–86.

    Google Scholar 

  12. Grubb, G., and Seeley, R. T.: Asymptotic expansions for the Atiyah-Patodi-Singer operator, C. R. Acad. Sci. Paris, Ser. I, 317 (1993), 1123–1126.

    Google Scholar 

  13. Grubb, G., and Seeley, R. T.: Weakly parametric pseudo Differential-operators and Atiyah-Patodi-Singer boundary-problems, Invent. Math. 121 (1995), 481–529.

    Google Scholar 

  14. Grubb, G., and Seeley, R. T.: Zeta and eta functions for Atiyah-Patodi-Singer operators, J. Geom. Anal. 6 (1996), 31–77.

    Google Scholar 

  15. McAvity, D. M.: Surface energy from heat content asymptotics, J. Phys. A: Math. Gen. 26 (1993), 823–830.

    Google Scholar 

  16. McDonald, P., and Meyers, R.: Dirichlet spectrum and heat content, J. Funct. Anal. 200 (2003), 150–159.

    Google Scholar 

  17. Savo, A.: Uniform estimates and the whole asymptotic series of the heat content on manifolds, Geom. Dedicata 73 (1998), 181–214.

    Google Scholar 

  18. Savo, A.: On the asymptotic series of the heat content. In: M. Ferández et al. (eds), Global Differential Geometry: the Mathematical Legacy of Alfred Gray, Proc. Internat. Congress on Differential Geometry, Bilbao, Spain, 18–23 September 2000 Contemp. Math. 288, Amer. Math. Soc., Providence, 2001, pp. 428-432.

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Gilkey, P., Kirsten, K. & Park, J.H. Heat Content Asymptotics for Operators of Laplace Type with Spectral Boundary Conditions. Letters in Mathematical Physics 68, 67–76 (2004). https://doi.org/10.1023/B:MATH.0000043236.80871.34

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  • DOI: https://doi.org/10.1023/B:MATH.0000043236.80871.34

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