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

Observations of nitrogen isotope fractionation in deeply embedded protostars

(Abridged) The terrestrial planets, comets, and meteorites are significantly enriched in 15N compared to the Sun and Jupiter. While the solar and jovian nitrogen isotope ratio is believed to represent the composition of the protosolar nebula, a still unidentified process has caused 15N-enrichment in the solids. Several mechanisms have been proposed to explain the variations, including chemical fractionation. However, observational results that constrain the fractionation models are scarce. While there is evidence of 15N-enrichment in prestellar cores, it is unclear how the signature evolves into the protostellar phases. Our aim is to measure the 14N/15N ratio around three nearby, embedded low-to-intermediate-mass protostars. Isotopologues of HCN and HNC were used to probe the 14N/15N ratio. A selection of H13CN, HC15N, HN13C, and H15NC transitions was observed with the APEX telescope. The 14N/15N ratios were derived from the integrated intensities assuming a standard 12C/13C ratio. The assumption of optically thin emission was verified using radiative transfer modeling and hyperfine structure fitting. Two sources, IRAS 16293A and R CrA IRS7B, show 15N-enrichment by a factor of around 1.5-2.5 in both HCN and HNC with respect to the solar composition. Solar composition cannot be excluded for the third source, OMC-3 MMS6. Furthermore, there are indications of a trend toward increasing 14N/15N ratios with increasing outer envelope temperature. The enhanced 15N abundances in HCN and HNC found in two Class~0 sources (14N/15N of 160-290) and the tentative trend toward a temperature-dependent 14N/15N ratio are consistent with the chemical fractionation scenario, but 14N/15N ratios from additional tracers are indispensable for testing the models. Spatially resolved observations are needed to distinguish between chemical fractionation and isotope-selective photochemistry.Comment: Accepted for publication in Astronomy and Astrophysics. 16 pages, 13 figure

Harmonic analysis of iterated function systems with overlap

In this paper we extend previous work on IFSs without overlap. Our method involves systems of operators generalizing the more familiar Cuntz relations from operator algebra theory, and from subband filter operators in signal processing.Comment: 37 page

Hot water in the inner 100 AU of the Class 0 protostar NGC1333 IRAS2A

Evaporation of water ice above 100 K in the inner few 100 AU of low-mass embedded protostars (the so-called hot core) should produce quiescent water vapor abundances of ~10^-4 relative to H2. Observational evidence so far points at abundances of only a few 10^-6. However, these values are based on spherical models, which are known from interferometric studies to be inaccurate on the relevant spatial scales. Are hot cores really that much drier than expected, or are the low abundances an artifact of the inaccurate physical models? We present deep velocity-resolved Herschel-HIFI spectra of the 3(12)-3(03) lines of H2-16O and H2-18O (1097 GHz, Eup/k = 249 K) in the low-mass Class 0 protostar NGC1333 IRAS2A. A spherical radiative transfer model with a power-law density profile is unable to reproduce both the HIFI data and existing interferometric data on the H2-18O 3(13)-2(20) line (203 GHz, Eup/k = 204 K). Instead, the HIFI spectra likely show optically thick emission from a hot core with a radius of about 100 AU. The mass of the hot core is estimated from the C18O J=9-8 and 10-9 lines. We derive a lower limit to the hot water abundance of 2x10^-5, consistent with the theoretical predictions of ~10^-4. The revised HDO/H2O abundance ratio is 1x10^-3, an order of magnitude lower than previously estimated.Comment: Accepted by ApJ; 12 pages in emulateapj format; 7 figure

Construction of Parseval wavelets from redundant filter systems

We consider wavelets in L^2(R^d) which have generalized multiresolutions. This means that the initial resolution subspace V_0 in L^2(R^d) is not singly generated. As a result, the representation of the integer lattice Z^d restricted to V_0 has a nontrivial multiplicity function. We show how the corresponding analysis and synthesis for these wavelets can be understood in terms of unitary-matrix-valued functions on a torus acting on a certain vector bundle. Specifically, we show how the wavelet functions on R^d can be constructed directly from the generalized wavelet filters.Comment: 34 pages, AMS-LaTeX ("amsproc" document class) v2 changes minor typos in Sections 1 and 4, v3 adds a number of references on GMRA theory and wavelet multiplicity analysis; v4 adds material on pages 2, 3, 5 and 10, and two more reference

An extension of Wiener integration with the use of operator theory

With the use of tensor product of Hilbert space, and a diagonalization procedure from operator theory, we derive an approximation formula for a general class of stochastic integrals. Further we establish a generalized Fourier expansion for these stochastic integrals. In our extension, we circumvent some of the limitations of the more widely used stochastic integral due to Wiener and Ito, i.e., stochastic integration with respect to Brownian motion. Finally we discuss the connection between the two approaches, as well as a priori estimates and applications.Comment: 13 page

ISO far-infrared observations of rich galaxy clusters II. Sersic 159-03

The far-infrared emission from rich galaxy clusters is investigated. Maps have been obtained by ISO at 60, 100, 135, and 200 microns using the PHT-C camera. Ground based imaging and spectroscopy were also acquired. Here we present the results for the cooling flow cluster Sersic 159-03. An infrared source coincident with the dominant cD galaxy is found. Some off-center sources are also present, but without any obvious counterparts.Comment: 6 pages, 4 postscript figures, accepted for publication in `Astronomy and Astrophysics