The resolvent expansion for second order regular singular operators

Brüning, Jochen; Seeley, R.

doi:10.1016/0022-1236(87)90073-5

Cited by 120 publications

(146 citation statements)

References 11 publications

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“…The main concern of [Ch3] is the L 2 -Hodge theory, whereas Peyerimhoff and Lesch [P], [LP] studied index problems for geometric operators on these spaces by extendending methods of regular singular analysis as developed by Briining and Seeley for conic singularities [BS1], [BS2]. They did not succeed, however, in proving a Signature Theorem; this we will do here.…”

Section: The Resultsmentioning

confidence: 99%

The signature theorem for manifolds with metric horns

Brüning¹

1996

Journées Équations Aux Dérivées Partielles

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Section: The Resultsmentioning

confidence: 99%

The signature theorem for manifolds with metric horns

Brüning¹

1996

Journées Équations Aux Dérivées Partielles

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“…Cheeger's theorem ( [4]) states that the spectrum, {λ k }, of ∆ m is discrete (with each eigenvalue having finite multiplicity) and its counting function, N (λ), obeys the standard spectral asymptotics N (λ) = O(|λ|) at the infinity. Moreover, from the results of Brüning and Seeley [2] it follows that the analytic continuation of the corresponding operator zeta-function…”

Section: Determinants Of Laplaciansmentioning

confidence: 94%

Genus one polyhedral surfaces, spaces of quadratic differentials on tori and determinants of Laplacians

Klochko

Kokotov

2006

manuscripta math.

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Abstract. We prove a formula for the determinant of Laplacian on an arbitrary compact polyhedral surface of genus one. This formula generalizes the well-known Ray-Singer result for a flat torus. A special case of flat conical metrics given by the modulus of a meromorphic quadratic differential on an elliptic surface is also considered. We study the determinant of Laplacian as a functional on the moduli space Q 1 (1, . . . , 1, [−1] L ) of meromorphic quadratic differentials with L simple poles and L simple zeros and derive formulas for variations of this functional with respect to natural coordinates on Q 1 (1, . . . , 1, [−1] L ). We give also a new proof of Troyanov's theorem stating the existence of a conformal flat conical metric on a compact Riemann surface of arbitrary genus with a prescribed divisor of conical points.

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“…We want to make the normal operator N(x 2 ∆ p ) y 0 explicit with respect to a rescaling of the form bundles, employed also in [BrSe87]. More precisely, for each j, l with j + l = p, we define…”

Section: Hodge Laplacian On Incomplete Edge Spacesmentioning

confidence: 99%

Heat-trace asymptotics for edge Laplacians with algebraic boundary conditions

Vertman

2015

JAMA

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Abstract. We consider the Hodge Laplace operator on manifolds with incomplete edge singularities and an intricate elliptic boundary value theory. We single out the class of algebraic self-adjoint extensions for the Hodge Laplacian. Our microlocal heat kernel construction for algebraic boundary conditions is guided by the method of signaling solutions by Mooers, though crucial arguments in the conical case obviously do not carry over to the setup of edges. We establish the heat kernel asymptotics for the algebraic extensions of the Hodge operator on edges, and elaborate on the exotic phenomena in the heat trace asymptotics which appear in the case of a non-Friedrichs extension.

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The resolvent expansion for second order regular singular operators

Cited by 120 publications

References 11 publications

The signature theorem for manifolds with metric horns

The signature theorem for manifolds with metric horns

Genus one polyhedral surfaces, spaces of quadratic differentials on tori and determinants of Laplacians

Heat-trace asymptotics for edge Laplacians with algebraic boundary conditions

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