## Essential . . . EIGENFORMS, AND SPECTRA FOR THE ¯∂-NEUMANN PROBLEM ON G-MANIFOLDS. (2011)

### BibTeX

@MISC{Perez11essential.,

author = {Joe J Perez and Peter Stollmann},

title = {Essential . . . EIGENFORMS, AND SPECTRA FOR THE ¯∂-NEUMANN PROBLEM ON G-MANIFOLDS.},

year = {2011}

}

### OpenURL

### Abstract

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.