Recent progress on truncated Toeplitz operators

This paper is a survey on the emerging theory of truncated Toeplitz operators. We begin with a brief introduction to the subject and then highlight the many recent developments in the field since Sarason's seminal paper in 2007.Comment: 46 page

Model spaces: a survey

This is a brief and gentle introduction, aimed at graduate students, to the subject of model subspaces of the Hardy space.Comment: 55 page

Partial orders on partial isometries

This paper studies three natural pre-orders of increasing generality on the set of all completely non-unitary partial isometries with equal defect indices. We show that the problem of determining when one partial isometry is less than another with respect to these pre-orders is equivalent to the existence of a bounded (or isometric) multiplier between two natural reproducing kernel Hilbert spaces of analytic functions. For large classes of partial isometries these spaces can be realized as the well-known model subspaces and deBranges-Rovnyak spaces. This characterization is applied to investigate properties of these pre-orders and the equivalence classes they generate.Comment: 30 pages. To appear in Journal of Operator Theor

Failed delivery and daily Treasury bill returns

If the seller of a Treasury bill does not provide timely and correct delivery instructions to the clearing bank, the bank does not deliver the security. Further, the seller is not paid until this "failed delivery" is rectified. Since the purchase price is not changed, these "fails" generate interest-free loans from the seller to the buyer. ; This paper studies the effect of failed delivery on Treasury-bill prices. We find that investors bid prices to a premium to reflect the possibility of obtaining the interest-free loans that fails represent. This premium is a function of the opportunity cost of the fail. We also find that the bid-ask spread varies directly with the length of the fail. We rule out the possibility that our results are due to liquidity premiums, or to a general weekly pattern in short-term interest rates or the bid-ask spread.Treasury bills

Real complex functions

We survey a few classes of analytic functions on the disk that have real boundary values almost everywhere on the unit circle. We explore some of their properties, various decompositions, and some connections these functions make to operator theory.Comment: 44 page

Transient gamma-ray emission from Cygnus X-3

The high-mass microquasar Cygnus X-3 has been recently detected in a flaring state by the gamma-ray satellites Fermi and Agile. In the present contribution, we study the high-energy emission from Cygnus X-3 through a model based on the interaction of clumps from the Wolf-Rayet wind with the jet. The clumps inside the jet act as obstacles in which shocks are formed leading to particle acceleration and non-thermal emission. We model the high energy emission produced by the interaction of one clump with the jet and briefly discus the possibility of many clumps interacting with the jet. From the characteristics of the considered scenario, the produced emission could be flare-like due to discontinuous clump penetration, with the GeV long-term activity explained by changes in the wind properties.Comment: Contribution to the proceedings of the 25th Texas Symposium on Relativistic Astrophysics - TEXAS 2010, December 06-10, Heidelberg, German

C∗C^*-algebras generated by truncated Toeplitz operators

We obtain an analogue of Coburn's description of the Toeplitz algebra in the setting of truncated Toeplitz operators. As a byproduct, we provide several examples of complex symmetric operators which are not unitarily equivalent to truncated Toeplitz operators having continuous symbols.Comment: 12 page

High-energy flares from jet-clump interactions

High-mass microquasars are binary systems composed by a massive star and a compact object from which relativistic jets are launched. Regarding the companion star, observational evidence supports the idea that winds of hot stars are formed by clumps. Then, these inhomogeneities may interact with the jets producing a flaring activity. In the present contribution we study the interaction between a jet and a clump of the stellar wind in a high-mass microquasar. This interaction produces a shock in the jet, where particles may be accelerated up to relativistic energies. We calculate the spectral energy distributions of the dominant non-thermal processes: synchrotron radiation, inverse Compton scattering, and proton-proton collisions. Significant levels of X- and gamma-ray emission are predicted, with luminosities in the different domains up to ~ 10^{34} - 10^{35} erg/s on a timescale of about ~ 1 h. Finally, jet-clump interactions in high-mass microquasars could be detectable at high energies. These phenomena may be behind the fast TeV variability found in some high-mass X-ray binary systems, such as Cygnus X-1, LS 5039 and LS I+61 303. In addition, our model can help to derive information on the properties of jets and clumpy winds.Comment: Proceeding of the conference "High Energy Phenomena in Massive Stars". Jaen (Spain), 2-5 February 200