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

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

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

Astrochemistry During the Formation of Stars

Star-forming regions show a rich and varied chemistry, including the presence of complex organic molecules - both in the cold gas distributed on large scales, and in the hot regions close to young stars where protoplanetary disks arise. Recent advances in observational techniques have opened new possibilities for studying this chemistry. In particular, the Atacama Large Millimeter/submillimeter Array (ALMA) has made it possible to study astrochemistry down to Solar System size scales, while also revealing molecules of increasing variety and complexity. In this review, we discuss recent observations of the chemistry of star-forming environments, with a particular focus on complex organic molecules, taking context from the laboratory experiments and chemical models that they have stimulated. The key takeaway points are: The physical evolution of individual sources plays a crucial role in their inferred chemical signatures, and remains an important area for observations and models to elucidate. Comparisons of the abundances measured toward different star-forming environments (high-mass versus low-mass, Galactic center versus Galactic disk) reveal a remarkable similarity, an indication that the underlying chemistry is relatively independent of variations in their physical conditions. Studies of molecular isotopologs in star-forming regions provide a link with measurements in our own Solar System, and thus may shed light on the chemical similarities and differences expected in other planetary systems.Comment: Invited review to be published in Annual Reviews of Astronomy and Astrophysics; 55 pages, 10 figure

Entropy Encoding, Hilbert Space and Karhunen-Loeve Transforms

By introducing Hilbert space and operators, we show how probabilities, approximations and entropy encoding from signal and image processing allow precise formulas and quantitative estimates. Our main results yield orthogonal bases which optimize distinct measures of data encoding.Comment: 25 pages, 1 figur

Effects of carbon incorporation on doping state of YBa2Cu3Oy

Effects of carbon incorporation on the doping state of YBa2Cu3Oy (Y-123) were investigated. Quantitative carbon analysis revealed that carbon could be introduced into Y-123 from both the precursor and the sintering gas. Nearly carbon-free (< 200 ppm) samples were prepared from a vacuum-treated precursor by sintered at 900 &#730;C and cooling with 20 &#730;C /min in flowing oxygen gas. The lower Tc (= 88 K) and higher oxygen content (y = 6.98) strongly suggested the overdoping state, which was supported by the temperature dependence of resisitivity and thermoelectric power. The nuclear quadrapole resonance spectra and the Raman scattering spectra indicated that there was almost no oxygen defect in the Cu-O chain in these samples. On the other hand, in the same cooling condition, the samples sintered in air stayed at optimal doping level with Tc = 93 K, and the intentionally carbon-doped sample was in the underdoping state. It is revealed that about 60% of incorporated carbon was substituted for Cu at the chain site in the form of CO32+, and the rest remains at the grain boundary as carbonate impurities. Such incorporation affected the oxygen absorption process in Y-123. It turned out that the oxygen content in Y-123 cannot be controlled only by the annealing temperature and the oxygen partial pressure but also by the incorporated carbon concentration.Comment: 16pages, 9figure

In-situ epitaxial growth of superconducting La-based bilayer cuprate thin films

We investigate the epitaxial growth of bilayer cuprate La2CaCu2O6+\delta using pure ozone as an oxidant, and find that even the crystal with parent composition without cation substitution can show metallic behavior with the aid of epitaxial strain effect. The hole concentration is controlled simply by excess-oxygen doping, and the films grown under the optimum conditions exhibit superconductivity below 30 K. This is the first result on the superconductivity of bilayer La2CaCu2O6+\delta induced purely by the excess oxygen.Comment: 5 pages, 3 figures, To appear in Phys. Rev. B, Rapid Communication