Weak products of complete Pick spaces

Let $\mathcal H$ be the Drury-Arveson or Dirichlet space of the unit ball of $\mathbb C^d$. The weak product $\mathcal H\odot\mathcal H$ of $\mathcal H$ is the collection of all functions $h$ that can be written as $h=\sum_{n=1}^\infty f_n g_n$, where $\sum_{n=1}^\infty \|f_n\|\|g_n\|<\infty$. We show that $\mathcal H\odot\mathcal H$ is contained in the Smirnov class of $\mathcal H$, i.e. every function in $\mathcal H\odot\mathcal H$ is a quotient of two multipliers of $\mathcal H$, where the function in the denominator can be chosen to be cyclic in $\mathcal H$. As a consequence we show that the map $\mathcal N \to clos_{\mathcal H\odot\mathcal H} \mathcal N$ establishes a 1-1 and onto correspondence between the multiplier invariant subspaces of $\mathcal H$ and of $\mathcal H\odot\mathcal H$. The results hold for many weighted Besov spaces $\mathcal H$ in the unit ball of $\mathbb C^d$ provided the reproducing kernel has the complete Pick property. One of our main technical lemmas states that for weighted Besov spaces $\mathcal H$ that satisfy what we call the multiplier inclusion condition any bounded column multiplication operator $\mathcal H \to \oplus_{n=1}^\infty \mathcal H$ induces a bounded row multiplication operator $\oplus_{n=1}^\infty \mathcal H \to \mathcal H$. For the Drury-Arveson space $H^2_d$ this leads to an alternate proof of the characterization of interpolating sequences in terms of weak separation and Carleson measure conditions.Comment: minor change

An HpH^p scale for complete Pick spaces

We define by interpolation a scale analogous to the Hardy $H^p$ scale for complete Pick spaces, and establish some of the basic properties of the resulting spaces, which we call $\mathcal{H}^p$. In particular, we obtain an $\mathcal{H}^p-\mathcal{H}^q$ duality and establish sharp pointwise estimates for functions in $\mathcal{H}^p$

Factorizations induced by complete Nevanlinna-Pick factors

We prove a factorization theorem for reproducing kernel Hilbert spaces whose kernel has a normalized complete Nevanlinna-Pick factor. This result relates the functions in the original space to pointwise multipliers determined by the Nevanlinna-Pick kernel and has a number of interesting applications. For example, for a large class of spaces including Dirichlet and Drury-Arveson spaces, we construct for every function $f$ in the space a pluriharmonic majorant of $|f|^2$ with the property that whenever the majorant is bounded, the corresponding function $f$ is a pointwise multiplier.Comment: 35 pages; minor change

Higgs Boson Production in Weak Boson Fusion at Next-to-Leading Order

The weak boson fusion process for neutral Higgs boson production is investigated with particular attention to the accuracy with which the Higgs boson coupling to weak bosons can be determined at CERN Large Hadron Collider (LHC) energies in final states that contain a Higgs boson plus at least two jets. Using fully differential perturbative matrix elements for the weak boson fusion signal process and for the QCD background processes, we generate events in which a Higgs boson is produced along with two jets that carry large transverse momentum. The effectiveness of different prescriptions to enhance the signal to background ratio is studied, and the expected signal purities are calculated in each case. We find that a simple cut on the rapidity of one final-state jet works well. We determine that an accuracy of delta_g/g ~ 10% on the effective coupling g may be possible after ~ 200 fb^-1 of integrated luminosity is accumulated at the LHC.Comment: 34 pages. Some restructuring of the text, a few sentences and one figure added. Conclusions not altered. To be published in Physical Review

A solvable model of a random spin-1/2 XY chain

The paper presents exact calculations of thermodynamic quantities for the spin-1/2 isotropic XY chain with random lorentzian intersite interaction and transverse field that depends linearly on the surrounding intersite interactions.Comment: 14 pages (Latex), 2 tables, 13 ps-figures included, (accepted for publication in Phys.Rev.B

Influence of soil properties on archaeal diversity and distribution in the McMurdo Dry Valleys, Antarctica

Archaea are the least understood members of the microbial community in Antarctic mineral soils. Although their occurrence in Antarctic coastal soils has been previously documented, little is known about their distribution in soils across the McMurdo Dry Valleys, Victoria Land. In this study, terminal-restriction fragment length polymorphism (t-RFLP) analysis and 454 pyrosequencing were coupled with a detailed analysis of soil physicochemical properties to characterize archaeal diversity and identify environmental factors that might shape and maintain archaeal communities in soils of the three southern most McMurdo Dry Valleys (Garwood, Marshall, and Miers Valley). Archaea were successfully detected in all inland and coastal mineral soils tested, revealing a low overall richness (mean of six operational taxonomic units [OTUs] per sample site). However, OTU richness was higher in some soils and this higher richness was positively correlated with soil water content, indicating water as a main driver of archaeal community richness. In total, 18 archaeal OTUs were detected, predominately Thaumarchaeota affiliated with Marine Group 1.1b (> 80% of all archaeal sequences recovered). Less abundant OTUs (2% of all archaeal sequences) were loosely related to members of the phylum Euryarchaeota. This is the first comprehensive study showing a widespread presence and distribution of Archaea in inland Antarctic soils

Smirnov class for spaces with the complete Pick property

We show that every function in a reproducing kernel Hilbert space with a normalized complete Pick kernel is the quotient of a multiplier and a cyclic multiplier. This extends a theorem of Alpay, Bolotnikov and Kaptanoğlu. We explore various consequences of this result regarding zero sets, spaces on compact sets and Gleason parts. In particular, using a construction of Salas, we exhibit a rotationally invariant complete Pick space of analytic functions on the unit disc for which the corona theorem fails

Multiplier tests and subhomogeneity of multiplier algebras

Multipliers of reproducing kernel Hilbert spaces can be characterized in terms of positivity of $n \times n$ matrices analogous to the classical Pick matrix. We study for which reproducing kernel Hilbert spaces it suffices to consider matrices of bounded size $n$. We connect this problem to the notion of subhomogeneity of non-selfadjoint operator algebras. Our main results show that multiplier algebras of many Hilbert spaces of analytic functions, such as the Dirichlet space and the Drury-Arveson space, are not subhomogeneous, and hence one has to test Pick matrices of arbitrarily large matrix size $n$. To treat the Drury-Arveson space, we show that multiplier algebras of certain weighted Dirichlet spaces on the disc embed completely isometrically into the multiplier algebra of the Drury-Arveson space.Comment: 39 page

Looking for Pure Rotational H_2 Emission from Protoplanetary Disks

We report on a limited search for pure-rotational molecular hydrogen emission associated with young, pre-main-sequence stars. We looked for H_2 v=0 J = 3->1 and J = 4->2 emission in the mid-infrared using the Texas Echelon-Cross-Echelle Spectrograph (TEXES) at NASA's 3m Infrared Telescope Facility. The high spectral and spatial resolution of our observations lead to more stringent limits on narrow line emission close to the source than previously achieved. One star, AB Aur, shows a possible (2sigma) H_2 detection, but further observations are required to make a confident statement. Our non-detections suggest that a significant fraction, perhaps all, of previously reported H_2 emission towards these objects could be extended on scales of 5" or more.Comment: 14 pages including 2 figures. Accepted by ApJ Letter

First Detection of HCO+^+ Absorption in the Magellanic System

We present the first detection of HCO$^+$ absorption in the Magellanic System. Using the Australia Telescope Compact Array (ATCA), we observed 9 extragalactic radio continuum sources behind the Magellanic System and detected HCO$^+$ absorption towards one source located behind the leading edge of the Magellanic Bridge. The detection is located at LSR velocity of $v=214.0 \pm 0.4\rm\,km\,s^{-1}$, with a full width at half maximum of $\Delta v=4.5\pm 1.0\rm\,km\,s^{-1}$ and optical depth of $\tau(\rm HCO^+)=0.10\pm 0.02$. Although there is abundant neutral hydrogen (HI) surrounding the sightline in position-velocity space, at the exact location of the absorber the HI column density is low, $<10^{20}\rm\,cm^{-2}$, and there is little evidence for dust or CO emission from Planck observations. While the origin and survival of molecules in such a diffuse environment remains unclear, dynamical events such as HI flows and cloud collisions in this interacting system likely play an important role.Comment: Accepted for publication in ApJ. 6 pages, 2 figures, 2 table