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Gluing formulae for heat kernels
Published 29 Mar 2024 in math-ph, math.AP, math.DG, and math.MP | (2404.00156v1)
Abstract: We state and prove two gluing formulae for the heat kernel of the Laplacian on a Riemannian manifold of the form $M_1 \cup_\gamma M_2$. We present several examples.
- L. Anderson, B. Driver, “Finite dimensional approximations to Wiener measure and path integral formulas on manifolds,” J. Funct. Anal. 165, 430–498 (1999).
- D. Burghelea, L. Friedlander, T. Kappeler, “Meyer-Vietoris type formula for determinants of elliptic differential operators,” J. Funct. Anal., 107.1 (1992) 34–65.
- N. Berline, E. Getzler, M. Vergne, “Heat kernels and Dirac operators,” 1992.
- Christian Baer, Frank Pfaeffle, “Wiener Measures on Riemannian Manifolds and the Feynman-Kac Formula”, Matematica Contemporanea 40 (2011), 37-90
- G. Carron, “Déterminant relatif et la fonction Xi,” Amer. J. Math., 124.2 (2002).
- A. P. Calderon, R. Vaillancourt. “On the boundedness of pseudo-differential operators.” J. Math. Soc. Japan 23 (2) 374 - 378, April, 1971. https://doi.org/10.2969/jmsj/02320374
- I. Contreras, S. Kandel, P. Mnev, K. Wernli, “Combinatorial QFT on graphs: first quantization formalism”. arXiv:2308.07801
- K. Costello, “Renormalization and Effective Field Theory”. Mathematical Surveys and Monographs, Volume 170, American Mathematical Society (2011)
- R. P. Feynman, A. R. Hibbs, “Quantum Mechanics and Path Integrals,” McGraw-Hill, New York (1965).
- Girouard, Alexandre, Mikhail Karpukhin, Michael Levitin, and Iosif Polterovich. 2022.“The Dirichlet-to-Neumann Map, the Boundary Laplacian, and Hörmander’s Rediscovered Manuscript,” Journal of Spectral Theory 12 (1): 195–225.
- Alexandre Girouard, Iosif Polterovich, “Spectral geometry of the Steklov problem (Survey article)”, J. Spectr. Theory 7 (2017), no. 2, pp. 321–359 New York, second edition, 1987.
- A. Grigor’yan, “Heat kernel on a non-compact Riemannian manifold.” (1993): 239–263.
- L. Hörmander, “Inequalities between normal and tangential derivatives of harmonic functions,” in: L. Hörmander, Unpublished manuscripts, Springer, 2018, 37–41. Riemannian setting,” Advances in Theoretical and Mathematical Physics 20.6 (2016): 1443–1471.
- F. Hanisch, A. Strohmaier, A. Waters, “A relative trace formula for obstacle scattering,” Duke Math. J. 171 (11), 2233-2274
- S. Kandel, P. Mnev, K. Wernli, “Two-dimensional perturbative scalar QFT and Atiyah–Segal gluing,” Advances in Theoretical and Mathematical Physics 25.7 (2021): 1847–1952
- M. E. Taylor. “Partial differential equations II. Qualitative studies of linear equations.” Applied Mathematical Sciences, Vol 116. Springer, New York, Second edition, 2011.
- G. Vodev, “High-frequency approximation of the interior Dirichlet-to-Neumann map and applications to the transmission eigenvalues, ” Anal. PDE 11(1): 213-236 (2018). DOI: 10.2140/apde.2018.11.213 The Clarendon Press, Oxford University Press, New York, 1992.
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