Brüning, J.; Seeley, R. The expansion of the resolvent near a singular stratum of conical type. (English) Zbl 0739.35043 J. Funct. Anal. 95, No. 2, 255-290 (1991). The authors consider a second order, formally self-adjoint elliptic operator \(\Delta\) with scalar principle symbol, on a manifold, having “conic” singularities along a compact submanifold. By considering first another “normal” operator whose inverse provides the first term in a Neumann series for the given operator — thought of as a perturbation of the normal operator — it becomes possible to represent \(tr(\Delta+\lambda)^{-m}\), \(\lambda\to\infty\), as an integral for suitably large \(m\), \((\Delta+\lambda)^{-m}\) being shown to be of trace class. Reviewer: R.Saxton (New Orleans) Cited in 1 ReviewCited in 21 Documents MSC: 35P05 General topics in linear spectral theory for PDEs 58J40 Pseudodifferential and Fourier integral operators on manifolds 35S15 Boundary value problems for PDEs with pseudodifferential operators Keywords:singular asymptotics; Zaremba problem; second order formally self-adjoint elliptic operator × Cite Format Result Cite Review PDF Full Text: DOI References: [1] Brüning, J.; Seeley, R., Regular singular asymptotics, Adv. in Math., 58, 133-148 (1985) · Zbl 0593.47047 [2] Brüning, J.; Seeley, R., The resolvent expansion for second order regular singular operators, J. Funct. Anal., 73, 369-429 (1987) · Zbl 0625.47040 [3] Calderón, A.; Vaillancourt, R., On the boundedness of pseudodifferential operators, J. Math. Soc. Japan, 23, 374-378 (1971) · Zbl 0203.45903 [4] Halmos, P.; Sunder, V., Bounded Integral Operators in \(L^2\) Spaces (1978), Springer: Springer Berlin · Zbl 0389.47001 [6] Seeley, R., The resolvent of an elliptic boundary problem, Amer. J. Math., 91, 889-920 (1969) · Zbl 0191.11801 [7] Magnus, W.; Oberhettinger, F.; Soni, R. P., Formulas and Theorems for the Special Functions of Mathematical Physics (1966), Springer-Verlag: Springer-Verlag Berlin, NY · Zbl 0143.08502 [9] Simanca, S., Mixed elliptic boundary value problems, Comm. Partial Differential Equations, 12, 123-200 (1987) · Zbl 0631.35024 [10] Watson, G., A Treatise on the Theory of Bessel Functions (1948), University Press: University Press Cambridge This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.