Iterated function systems, representations, and Hilbert space

This paper studies a general class of Iterated Function Systems (IFS). No contractivity assumptions are made, other than the existence of some compact attractor. The possibility of escape to infinity is considered. Our present approach is based on Hilbert space, and the theory of representations of the Cuntz algebras O_n, n=2,3,.... While the more traditional approaches to IFS's start with some equilibrium measure, ours doesn't. Rather, we construct a Hilbert space directly from a given IFS; and our construction uses instead families of measures. Starting with a fixed IFS S_n, with n branches, we prove existence of an associated representation of O_n, and we show that the representation is universal in a certain sense. We further prove a theorem about a direct correspondence between a given system S_n, and an associated sub-representation of the universal representation of O_n.Comment: 22 pages, 3 figures containing 7 EPS graphics; LaTeX2e ("elsart" document class); v2 reflects change in Comments onl

Commuting self-adjoint extensions of symmetric operators defined from the partial derivatives

We consider the problem of finding commuting self-adjoint extensions of the partial derivatives {(1/i)(\partial/\partial x_j):j=1,...,d} with domain C_c^\infty(\Omega) where the self-adjointness is defined relative to L^2(\Omega), and \Omega is a given open subset of R^d. The measure on \Omega is Lebesgue measure on R^d restricted to \Omega. The problem originates with I.E. Segal and B. Fuglede, and is difficult in general. In this paper, we provide a representation-theoretic answer in the special case when \Omega=I\times\Omega_2 and I is an open interval. We then apply the results to the case when \Omega is a d-cube, I^d, and we describe possible subsets \Lambda of R^d such that {e^(i2\pi\lambda \dot x) restricted to I^d:\lambda\in\Lambda} is an orthonormal basis in L^2(I^d).Comment: LaTeX2e amsart class, 18 pages, 2 figures; PACS numbers 02.20.Km, 02.30.Nw, 02.30.Tb, 02.60.-x, 03.65.-w, 03.65.Bz, 03.65.Db, 61.12.Bt, 61.44.B

Reflection positive affine actions and stochastic processes

In this note we continue our investigations of the representation theoretic aspects of reflection positivity, also called Osterwalder--Schrader positivity. We explain how this concept relates to affine isometric actions on real Hilbert spaces and how this is connected with Gaussian processes with stationary increments

Charge exchange contribution to the decay of the ring current, measured by energetic neutral atoms (ENAs)

In this paper we calculate the contribution of charge exchange to the decay of the ring current. Past works have suggested that charge exchange of ring current protons is primarily responsible for the decay of the ring current during the late recovery phase, but there is still much debate about the fast decay of the early recovery phase. We use energetic neutral atom (ENA) measurements from Polar to calculate the total ENA energy escape. To get the total ENA escape we apply a forward modeling technique, and to estimate the total ring current energy escape we use the Dessler-Parker-Sckopke relationship. We find that during the late recovery phase of the March 10, 1998 storm ENAs with energies greater than 17.5 keV can account for 75% of the estimated energy loss from the ring current. During the fast recovery the measured ENAs can only account for a small portion of the total energy loss. We also find that the lifetime of the trapped ions is significantly shorter during the fast recovery phase than during the late recovery phase, suggesting that different processes are operating during the two phases

Global energetic neutral atom (ENA) measurements and their association with the Dst index

We present a new global magnetospheric index that measures the intensity of the Earth\u27s ring current through energetic neutral atoms (ENAs). We have named it the Global Energetic Neutral Index (GENI), and it is derived from ENA measurements obtained by the Imaging Proton Spectrometer (IPS), part of the Comprehensive Energetic Particle and Pitch Angle Distribution (CEPPAD) experiment on the POLAR satellite. GENI provides a simple orbit-independent global sum of ENAs measured with IPS. Actual ENA measurements for the same magnetospheric state look different when seen from different points in the POLAR orbit. In addition, the instrument is sensitive to weak ion populations in the polar cap, as well as cosmic rays. We have devised a method for removing the effects of cosmic rays and weak ion fluxes, in order to produce an image of “pure” ENA counts. We then devised a method of normalizing the ENA measurements to remove the orbital bias effect. The normalized data were then used to produce the GENI. We show, both experimentally and theoretically the approximate proportionality between the GENI and the Dst index. In addition we discuss possible implications of this relation. Owing to the high sensitivity of IPS to ENAs, we can use these data to explore the ENA/Dst relationship not only during all phases of moderate geomagnetic storms, but also during quiescent ring current periods

Near-Infrared Imaging of Early-Type Galaxies III. The Near-Infrared Fundamental Plane

Near-infrared imaging data on 251 early-type galaxies in clusters and groups are used to construct the near-infrared Fundamental Plane (FP) r_eff ~ sigma_0^1.53 _eff^-0.79. The slope of the FP therefore departs from the virial expectation of r_eff ~ sigma_0^2 _eff^-1 at all optical and near-infrared wavelengths, which could be a result of the variation of M/L along the elliptical galaxy sequence, or a systematic breakdown of homology among the family of elliptical galaxies. The slope of the near-infrared FP excludes metallicity variations as the sole cause of the slope of the FP. Age effects, dynamical deviations from a homology, or any combination of these (with or without metallicity), however, are not excluded. The scatter of both the near-infrared and optical FP are nearly identical and substantially larger than the observational uncertainties, demonstrating small but significant intrinsic cosmological scatter for the FP at all wavelengths. The lack of a correlation of the residuals of the near-infrared FP and the residuals from the Mg_2-sigma relation indicates that the thickness of these relations cannot be ascribed only to age or metallicity effects. Due to this metallicity independence, the small scatter of the near-infrared FP excludes a model in which age and metallicity effects ``conspire'' to keep the optical FP thin. All of these results suggest that the possible physical origins of the FP relations are complicated due to combined effects of variations of stellar populations and structural parameters among elliptical galaxies.Comment: to appear in The Astronomical Journal; 35 pages, including 13 Postscript figures and 1 table; uses AAS LaTeX style file

The impact of shocks on the chemistry of molecular clouds: high resolution images of chemical differentiation along the NGC1333-IRAS2A outflow

This paper presents a detailed study of the chemistry in the outflow associated with the low-mass protostar NGC1333-IRAS2A down to 3" (650 AU) scales. Millimeter-wavelength aperture-synthesis observations from the OVRO and BIMA interferometers and (sub)millimeter single-dish observations from the Onsala 20m telescope and CSO are presented. The interaction of the highly collimated protostellar outflow with a molecular condensation ~15000 AU from the central protostar is clearly traced by molecular species such as HCN, SiO, SO, CS, and CH3OH. Especially SiO traces a narrow high velocity component at the interface between the outflow and the molecular condensation. Multi-transition single-dish observations are used to distinguish the chemistry of the shock from that of the molecular condensation and to address the physical conditions therein. Statistical equilibrium calculations reveal temperatures of 20 and 70 K for the quiescent and shocked components, respectively, and densities near 10^6 cm^{-3}. Significant abundance enhancements of two to four orders of magnitude are found in the shocked region for molecules such as CH3OH, SiO and the sulfur-bearing molecules. HCO+ is seen only in the aftermath of the shock consistent with models where it is destroyed through release of H2O from grain mantles in the shock. N2H+ shows narrow lines, not affected by the outflow but rather probing the ambient cloud. Differences in abundances of HCN, H2CO and CS are seen between different outflow regions and are suggested to be related to differences in the atomic carbon abundance. Compared to the warm inner parts of protostellar envelopes, higher abundances of in particular CH3OH and SiO are found in the outflows, which may be related to density differences between the regions.Comment: 18 pages, 13 figures. Accepted for publication in A&

The Fundamental Plane at z=1.27: First Calibration of the Mass Scale of Red Galaxies at Redshifts z>1

We present results on the Fundamental Plane (FP) of early-type galaxies in the cluster RDCS J0848+4453 at z=1.27. Internal velocity dispersions of three K-selected early-type galaxies are determined from deep Keck spectra. Structural parameters are determined from HST NICMOS images. The galaxies show substantial offsets from the FP of the nearby Coma cluster, as expected from passive evolution of their stellar populations. The offsets from the FP can be expressed as offsets in M/L ratio. The M/L ratios of the two most massive galaxies are consistent with an extrapolation of results obtained at z=0.02-0.83. The evolution of early-type galaxies with masses >10^11 M_sun is well described by ln M/L(B) = (-1.06 +- 0.09) z, corresponding to passive evolution of -1.50 +- 0.13 mag at z=1.3. Ignoring selection effects, the best fitting stellar formation redshift is z*=2.6, corresponding to a luminosity weighted age at the epoch of observation of ~2 Gyr. The M/L ratios of these two galaxies are also in excellent agreement with predictions from models that include progenitor bias. The third galaxy is a factor ~10 less massive than the other two, shows strong Balmer absorption lines in its spectrum, and is offset from the Coma Fundamental Plane by 2.9 mag in rest-frame B. Despite their large range in M/L ratios, all three galaxies fall in the ``Extremely Red Object'' (ERO) class with I-H>3 and R-K>5, and our results show that it is hazardous to use simple models for converting luminosity to mass for these objects. Measurements of M/L ratios at high redshift can be considered first steps to empirically disentangle luminosity and mass evolution at the high mass end of the galaxy population, lifting an important degeneracy in the interpretation of evolution of the luminosity function. [SHORTENED]Comment: Accepted for publication in the Astrophysical Journa