Elementary proofs of Paley-Wiener theorems for the Dunkl transform on the real line

We give an elementary proof of the Paley-Wiener theorem for smooth functions for the Dunkl transforms on the real line, establish a similar theorem for L^2-functions and prove identities in the spirit of Bang for L^p-functions. The proofs seem to be new also in the special case of the Fourier transform.Comment: 9 pp., LaTeX, no figures; final version, to appear in Int. Math. Res. No

Real Paley-Wiener theorems and local spectral radius formulas

We systematically develop real Paley-Wiener theory for the Fourier transform on R^d for Schwartz functions, L^p-functions and distributions, in an elementary treatment based on the inversion theorem. As an application, we show how versions of classical Paley-Wiener theorems can be derived from the real ones via an approach which does not involve domain shifting and which may be put to good use for other transforms of Fourier type as well. An explanation is also given why the easily applied classical Paley-Wiener theorems are unlikely to be able to yield information about the support of a function or distribution which is more precise than giving its convex hull, whereas real Paley-Wiener theorems can be used to reconstruct the support precisely, albeit at the cost of combinatorial complexity. We indicate a possible application of real Paley-Wiener theory to partial differential equations in this vein and furthermore we give evidence that a number of real Paley-Wiener results can be expected to have an interpretation as local spectral radius formulas. A comprehensive overview of the literature on real Paley-Wiener theory is included.Comment: 27 pages, no figures. Reference updated. Final version, to appear in Trans. Amer. Math. So

Local spectral radius formulas for a class of unbounded operators on Banach spaces

We exhibit a general class of unbounded operators in Banach spaces which can be shown to have the single-valued extension property, and for which the local spectrum at suitable points can be determined. We show that a local spectral radius formula holds, analogous to that for a globally defined bounded operator on a Banach space with the single-valued extension property. An operator of the class under consideration can occur in practice as (an extension of) a differential operator which, roughly speaking, can be diagonalised on its domain of smooth test functions via a discrete transform, such that the diagonalising transform establishes an isomorphism of topological vector spaces between the domain of the differential operator, in its own topology, and a sequence space. We give concrete examples of (extensions of) such operators (constant coefficient differential operators on the d-torus, Jacobi operators, the Hermite operator, Laguerre operators) and indicate further perspectives.Comment: Minor changes in presentation. 23 pages, final version, to appear in Journal of Operator Theor

Orbital fluctuations in the different phases of LaVO3 and YVO3

We investigate the importance of quantum orbital fluctuations in the orthorhombic and monoclinic phases of the Mott insulators LaVO3 and YVO3. First, we construct ab-initio material-specific t2g Hubbard models. Then, by using dynamical mean-field theory, we calculate the spectral matrix as a function of temperature. Our Hubbard bands and Mott gaps are in very good agreement with spectroscopy. We show that in orthorhombic LaVO3, quantum orbital fluctuations are strong and that they are suppressed only in the monoclinic 140 K phase. In YVO3 the suppression happens already at 300 K. We show that Jahn-Teller and GdFeO3-type distortions are both crucial in determining the type of orbital and magnetic order in the low temperature phases.Comment: 4 pages, 3 figures, final version. To appear in PR

Eye muscle proprioception is represented bilaterally in the sensorimotor cortex

The cortical representation of eye position is still uncertain. In the monkey a proprioceptive representation of the extraocular muscles (EOM) of an eye were recently found within the contralateral central sulcus. In humans, we have previously shown a change in the perceived position of the right eye after a virtual lesion with rTMS over the left somatosensory area. However, it is possible that the proprioceptive representation of the EOM extends to other brain sites, which were not examined in these previous studies. The aim of this fMRI study was to sample the whole brain to identify the proprioceptive representation for the left and the right eye separately. Data were acquired while passive eye movement was used to stimulate EOM proprioceptors in the absence of a motor command. We also controlled for the tactile stimulation of the eyelid by removing from the analysis voxels activated by eyelid touch alone. For either eye, the brain area commonly activated by passive and active eye movement was located bilaterally in the somatosensory area extending into the motor and premotor cytoarchitectonic areas. We suggest this is where EOM proprioception is processed. The bilateral representation for either eye contrasts with the contralateral representation of hand proprioception. We suggest that the proprioceptive representation of the two eyes next to each other in either somatosensory cortex and extending into the premotor cortex reflects the integrative nature of the eye position sense, which combines proprioceptive information across the two eyes with the efference copy of the oculomotor comman

NNLO hard-thermal-loop thermodynamics for QCD

We calculate the thermodynamic functions of a quark-gluon plasma for general N_c and N_f to three-loop order using hard-thermal-loop perturbation theory. At this order, all the ultraviolet divergences can be absorbed into renormalizations of the vacuum, the HTL mass parameters, and the strong coupling constant.We show that at three loops, the results for the pressure and trace anomaly are in very good agreement with recent lattice data down to temperatures T~2T_c.Comment: 8 pages, 2 fig

On the (in)variance of the dust-to-metals ratio in galaxies

Recent works have demonstrated a surprisingly small variation of the dust-to-metals ratio in different environments and a correlation between dust extinction and the density of stars. Naively, one would interpret these findings as strong evidence of cosmic dust being produced mainly by stars. But other observational evidence suggest there is a significant variation of the dust-to-metals ratio with metallicity. As we demonstrate in this paper, a simple star-dust scenario is problematic also in the sense that it requires that destruction of dust in the interstellar medium (e.g., due to passage of supernova shocks) must be highly inefficient. We suggest a model where stellar dust production is indeed efficient, but where interstellar dust growth is equally important and acts as a replenishment mechanism which can counteract the effects of dust destruction. This model appears to resolve the seemingly contradictive observations, given that the ratio of the effective (stellar) dust and metal yields is not universal and thus may change from one environment to another, depending on metallicity.Comment: 10 pages, 4 figures. Accepted for publication in MNRA

The DiskMass Survey. I. Overview

We present a survey of the mass surface-density of spiral disks, motivated by outstanding uncertainties in rotation-curve decompositions. Our method exploits integral-field spectroscopy to measure stellar and gas kinematics in nearly face-on galaxies sampled at 515, 660, and 860 nm, using the custom-built SparsePak and PPak instruments. A two-tiered sample, selected from the UGC, includes 146 nearly face-on galaxies, with B<14.7 and disk scale-lengths between 10 and 20 arcsec, for which we have obtained H-alpha velocity-fields; and a representative 46-galaxy subset for which we have obtained stellar velocities and velocity dispersions. Based on re-calibration of extant photometric and spectroscopic data, we show these galaxies span factors of 100 in L(K) (0.03 < L/L(K)* < 3), 8 in L(B)/L(K), 10 in R-band disk central surface-brightness, with distances between 15 and 200 Mpc. The survey is augmented by 4-70 micron Spitzer IRAC and MIPS photometry, ground-based UBVRIJHK photometry, and HI aperture-synthesis imaging. We outline the spectroscopic analysis protocol for deriving precise and accurate line-of-sight stellar velocity dispersions. Our key measurement is the dynamical disk-mass surface-density. Star-formation rates and kinematic and photometric regularity of galaxy disks are also central products of the study. The survey is designed to yield random and systematic errors small enough (i) to confirm or disprove the maximum-disk hypothesis for intermediate-type disk galaxies, (ii) to provide an absolute calibration of the stellar mass-to-light ratio well below uncertainties in present-day stellar-population synthesis models, and (iii) to make significant progress in defining the shape of dark halos in the inner regions of disk galaxies.Comment: To appear in ApJ; 72 pages, 3 tables, 18 figures. High-resolution version available at http://www.astro.wisc.edu/~mab/publications/DMS_I_preprint.pd