1,706 research outputs found
Template iterations with non-definable ccc forcing notions
We present a version with non-definable forcing notions of Shelah's theory of
iterated forcing along a template. Our main result, as an application, is that,
if is a measurable cardinal and are
uncountable regular cardinals, then there is a ccc poset forcing
. Another
application is to get models with large continuum where the groupwise-density
number assumes an arbitrary regular value.Comment: To appear in the Annals of Pure and Applied Logic, 45 pages, 2
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Restrictions and extensions of semibounded operators
We study restriction and extension theory for semibounded Hermitian operators
in the Hardy space of analytic functions on the disk D. Starting with the
operator zd/dz, we show that, for every choice of a closed subset F in T=bd(D)
of measure zero, there is a densely defined Hermitian restriction of zd/dz
corresponding to boundary functions vanishing on F. For every such restriction
operator, we classify all its selfadjoint extension, and for each we present a
complete spectral picture.
We prove that different sets F with the same cardinality can lead to quite
different boundary-value problems, inequivalent selfadjoint extension
operators, and quite different spectral configurations. As a tool in our
analysis, we prove that the von Neumann deficiency spaces, for a fixed set F,
have a natural presentation as reproducing kernel Hilbert spaces, with a
Hurwitz zeta-function, restricted to FxF, as reproducing kernel.Comment: 63 pages, 11 figure
Middle divisors and -palindromic Dyck words
Given a real number , we say that is a -middle
divisor of if We
will prove that there are integers having an arbitrarily large number of
-middle divisors. Consider the word given by where is the set of
divisors of , and are the elements of the symmetric difference written in increasing order. We will prove that the language contains Dyck words having an
arbitrarily large number of centered tunnels. We will show a connection between
both results
Seshadri constants, Diophantine approximation, and Roth's Theorem for arbitrary varieties
In this paper, we associate an invariant to an algebraic
point on an algebraic variety with an ample line bundle . The
invariant measures how well can be approximated by rational points
on , with respect to the height function associated to . We show that
this invariant is closely related to the Seshadri constant
measuring local positivity of at , and in particular that Roth's theorem
on generalizes as an inequality between these two invariants
valid for arbitrary projective varieties.Comment: 55 pages, published versio
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