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**1 - 4**of**4**### A dual characterization of length spaces with application to Dirichlet metric spaces

, 2009

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### Essential self-adjointness, generalized eigenforms, and . . .

, 2011

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### Essential . . . EIGENFORMS, AND SPECTRA FOR THE ¯∂-NEUMANN PROBLEM ON G-MANIFOLDS.

, 2011

"... Let M be a complex manifold with boundary, satisfying a subelliptic estimate, which is also the total space of a principal G–bundle with G a Lie group and compact orbit space M — /G. Here we investigate the ¯ ∂-Neumann Laplacian □ on M. We show that it is essentially self-adjoint on its restrictio ..."

Abstract
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Let M be a complex manifold with boundary, satisfying a subelliptic estimate, which is also the total space of a principal G–bundle with G a Lie group and compact orbit space M — /G. Here we investigate the ¯ ∂-Neumann Laplacian □ on M. We show that it is essentially self-adjoint on its restriction to compactly supported smooth forms. Moreover we relate its spectrum to the existence of generalized eigenforms: an energy belongs to σ(□) if there is a subexponentially bounded generalized eigenform for this energy. Vice versa, there is an expansion in terms of these well–behaved eigenforms so that, spectrally, almost every energy comes with such a generalized eigenform.