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References
Agmon, S.: Lectures on elliptic boundary value problems. Princeton: Van Nostrand 1965
Brüning, J.: Invariant eigenfunctions of the Laplacian and their asymptotic distribution. In: Global differential geometry and global analysis. Lecture Notes in Mathematics, Vol. 838. Berlin, Heidelber, New York: Springer 1981
Brüning, J.: On the eigenvalue problem of t'Hooft. Manuscripta Math.,39, 126–146 (1982)
Brüning, J., Heintze, E.: The asymptotic expansion of Minakshisundaram-Pleijel in the equivariant case. To appear
Callias, C.: The heat equation with singular coefficients. I. Operators of the from\( - \frac{{d^2 }}{{dx^2 }} + \frac{\kappa }{{x^2 }}\) in dimension 1. Commun. Math. Phys.88, 357–385 (1983)
Cheeger, J.: On the spectral geometry of spaces with conelike singularities. Proc. Nat. Acad. Sci. USA76, 2103–2106 (1979)
Dunford, N., Schwartz, J.T.: Linear operators, Vols. I–III. New York: Interscience 1963
Jörgens, K., Rellich, F.: Eigenwerttheorie gewöhnlicher Differentialgleichungen. Berlin, Heidelberg, New York: Springer 1976
McKean, H., Singer, I.: Curvature and the eigenvalues of the Laplacian. J. Differential Geometry,1, 43–69 (1967)
Minakshisundaram, S., Pleijel, Å.: Some properties of the eigenfunctions of the Laplaceoperator on Riemannian manifolds. Canad. J. Math. 242–256 (1949)
Rellich, F.: Halbbeschränkte gewöhnliche Differentialoperatoren zweiter Ordnung. Math. Ann.122, 343–368 (1951)
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Brüning, J. Heat equation asymptotics for singular sturm-Liouville operators. Math. Ann. 268, 173–196 (1984). https://doi.org/10.1007/BF01456084
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DOI: https://doi.org/10.1007/BF01456084