54 research outputs found
On the Number of Unbordered Factors
We illustrate a general technique for enumerating factors of k-automatic
sequences by proving a conjecture on the number f(n) of unbordered factors of
the Thue-Morse sequence. We show that f(n) = 4 and that f(n) = n
infinitely often. We also give examples of automatic sequences having exactly 2
unbordered factors of every length
On unitarizability in the case of classical p-adic groups
In the introduction of this paper we discuss a possible approach to the
unitarizability problem for classical p-adic groups. In this paper we give some
very limited support that such approach is not without chance. In a forthcoming
paper we shall give additional evidence in generalized cuspidal rank (up to)
three.Comment: This paper is a merged and revised version of ealier preprints
arXiv:1701.07658 and arXiv:1701.07662. The paper is going to appear in the
Proceedings of the Simons Symposium on Geometric Aspects of the Trace Formul
Threshold and linewidth of a mirrorless parametric oscillator
We analyze the above-threshold behavior of a mirrorless parametric oscillator
based on resonantly enhanced four wave mixing in a coherently driven dense
atomic vapor. It is shown that, in the ideal limit, an arbitrary small flux of
pump photons is sufficient to reach the oscillator threshold. We demonstrate
that due to the large group-velocity delays associated with coherent media, an
extremely narrow oscillator linewidth is possible, making a narrow-band source
of non-classical radiation feasible.Comment: revised version to appear in Phys.Rev.Lett., contains discussion on
threshold conditions and operation on few-photon leve
Homological algebra for Schwartz algebras of reductive p-adic groups
Let G be a reductive group over a non-Archimedean local field. Then the
canonical functor from the derived category of smooth tempered representations
of G to the derived category of all smooth representations of G is fully
faithful. Here we consider representations on bornological vector spaces. As a
consequence, if V and W are two tempered irreducible representations and if V
or W is square-integrable, then Ext_G^n(V,W) vanishes for all n>0. We use this
to prove in full generality a formula for the formal dimension of
square-integrable representations due to Schneider and Stuhler.Comment: 34 pages, version 2 contains, in addition, a discussion about formal
dimensions from the point of view of Schwartz algebras and von Neumann
algebra
On limit multiplicites of discrete series representations in spaces of automorphic forms
Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/46616/1/222_2005_Article_BF01388963.pd
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