ZZH coupling : A probe to the origin of EWSB ?
Choudhury, Debajyoti
2003-02-17
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We show that under minimal assumptions, the intrinsic metric induced by a
strongly local Dirichlet form induces a length space. A main input is a dual
characterization of length spaces in terms of the property that the 1-Lipschitz
functions form a sheaf.
Comment: v3: final version, typos corrected; v2: references and some comments
added; to appear in "Boundaries and spectra of random walks," proceedings of
the Alp workshop Graz - St. Kathrein 2009, edited by D. Lenz, F. Sobieczky,
W. Woess
Comment: 19 pages; revised version
We show that geometric disorder leads to purely singular continuous spectrum
generically.
The main input is a result of Simon known as the ``Wonderland theorem''.
Here, we provide an alternative approach and actually a slight strengthening by
showing that various sets of measures defined by regularity properties are
generic in the set of all measures on a locally compact metric space.
As a byproduct we obtain that a generic measure on euclidean space is
singular continuous.
Comment: 16 pages, typos corrected, to appear in J. Funct. Anal
Let $M$ be a strongly pseudoconvex complex manifold which is also the total
space of a principal $G$-bundle with $G$ a Lie group and compact orbit space
$\bar M/G$. Here we investigate the $\bar\partial$-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 $\sigma(\square)$ 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.
The existence of positive weak solutions is related to spectral information
on the corresponding partial differential operator.
Comment: 11 pages, submitted to Jounal of Integral Equations and Operator
Theory
