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Intrinsic metrics for nonlocal symmetric Dirichlet forms and applications to spectral theory. to appear
, 2010
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Generalized solutions and spectrum for Dirichlet forms on graphs
 Progress in Probability
, 2011
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A dual characterization of length spaces with application to Dirichlet metric spaces
, 2009
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Generalized eigenfunctions and spectral theory for strongly local Dirichlet forms
, 2009
"... We present an introduction to the framework of strongly local Dirichlet forms and discuss connections between the existence of certain generalized eigenfunctions and spectral properties within this framework. The range of applications is illustrated by a list of examples. ..."
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We present an introduction to the framework of strongly local Dirichlet forms and discuss connections between the existence of certain generalized eigenfunctions and spectral properties within this framework. The range of applications is illustrated by a list of examples.
Essential selfadjointness, generalized eigenforms, and . . .
, 2011
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Essential . . . EIGENFORMS, AND SPECTRA FOR THE ¯∂NEUMANN PROBLEM ON GMANIFOLDS.
, 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 selfadjoint on its restrictio ..."
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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 selfadjoint 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.
Mathematisches Forschungsinstitut Oberwolfach Report No. 16/2008 Disordered Systems: Random Schrödinger Operators and Random Matrices
, 2008
"... Abstract. The spectral analysis of random operators plays a central role for the understanding of quantum systems with disorder. Two distinct types of ensembles are of particular significance: Random Schrödinger operators and random matrices. The workshop brought together experts from both areas to ..."
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Abstract. The spectral analysis of random operators plays a central role for the understanding of quantum systems with disorder. Two distinct types of ensembles are of particular significance: Random Schrödinger operators and random matrices. The workshop brought together experts from both areas to discuss recent results and future directions of research. Mathematics Subject Classification (2000): 15xx, 34xx, 35xx, 47xx, 60xx, 81xx, 82xx. Introduction by the Organisers It is natural to model the spectral behaviour of disordered quantum systems by the typical spectral properties of random operators. Depending on the underlying physics different kinds of ensembles have been introduced. Two types of ensembles, random Schrödinger operators and random matrices, have proved to be of