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

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

Science education on the U.S./Mexico border: Field-based studies for future teachers in bilingual/binational schools

The University of Texas at El Paso’s field-based program of studies for future teachers provides opportunities for powerful learning through a dialectical union of reflection and action. Methods courses in academic disciplines are linked with seminars and coursework on community partnerships, dual language education and culturally responsive education. This article illustrates the processes of planning, implementation and evaluation of this approach, highlighting the impacts of forging connections among schools, communities and university personnel to improve education on the U.S./Mexico border and in communities with culturally/linguistically diverse student populations. Parents, students and future teachers interact in bilingual workshops that center on pupil achievement and conceptually correct science education. Preliminary outcomes indicate that two-way dual language (TWDL) bilingual programs (i.e., validating native language literacy along with English language acquisition) with a strong parental engagement component provide a strong framework for teaching/learning that can help improve educational outcomes for ELL/immigrant children and deepen future teachers’ skills and knowledge. Focusing on academic enrichment for all students, these field-based experiences enable future teachers to learn strategies that integrate students’ and families’ linguistic and cultural experiences as a resource for learning. The co-authors highlight qualitative data findings from the Science in Our Homes – Ciencia en Nuestras Casas field-based project in a multilingual, multicultural K-8 school on the U.S./Mexico border, providing insights for educators in diverse communities whose efforts focus on closing the achievement gap for English language learners and/or immigrant students

Gravitational Binding, Virialization and the Peculiar Velocity Distribution of the Galaxies

We examine the peculiar velocity distribution function of galaxies in cosmological many-body gravitational clustering. Our statistical mechanical approach derives a previous basic assumption and generalizes earlier results to galaxies with haloes. Comparison with the observed peculiar velocity distributions indicates that individual massive galaxies are usually surrounded by their own haloes, rather than being embedded in common haloes. We then derive the density of energy states, giving the probability that a randomly chosen configuration of N galaxies in space is bound and virialized. Gravitational clustering is very efficient. The results agree well with the observed probabilities for finding nearby groups containing N galaxies. A consequence is that our local relatively low mass group is quite typical, and the observed small departures from the local Hubble flow beyond our group are highly probable.Comment: Paper in aastex 5.0 format and 9 figures. Replace a new version with figures and typos correcte

Agricultural Price Distortion and Stabilization: Stylized facts and Hypothesis Tests

This paper describes agricultural policy choices and tests some predictions of political economy theories. It begins with three broad stylized facts: governments tend to tax agriculture in poorer countries, and subsidize it in richer ones, tax both imports and exports more than nontradables, and tax more and subsidize less where there is more land per capita. We test a variety of political-economy explanations, finding results consistent with hypothesized effects of rural and urban constituents’ rational ignorance about small per-person effects, governance institutions’ control of rent-seeking by political leaders, governments’ revenue motive for taxation, and the role of time consistency in policy-making. We also find that larger groups obtain more favorable policies, suggesting that positive group size effects outweigh any negative influence from more free-ridership, and that demographically driven entry of new farmers is associated with less favorable farm policies, suggesting the arrival of new farmers erodes policy rents and discourages political activity by incumbents. Another new result is that governments achieve very little price stabilization relative to our benchmark estimates of undistorted prices, and governments in the poorest countries actually destabilize domestic prices.Distorted incentives, agricultural and trade policy reforms, national agricultural development, Agricultural price distortions, political economy, Agricultural and Food Policy, International Relations/Trade, F13, F14, Q17, Q18, D72, D78, F11, H23,

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

Unitary equivalence to a truncated Toeplitz operator: analytic symbols

Unlike Toeplitz operators on $H^2$, truncated Toeplitz operators do not have a natural matricial characterization. Consequently, these operators are difficult to study numerically. In this note we provide criteria for a matrix with distinct eigenvalues to be unitarily equivalent to a truncated Toeplitz operator having an analytic symbol. This test is constructive and we illustrate it with several examples. As a byproduct, we also prove that every complex symmetric operator on a Hilbert space of dimension $\leq 3$ is unitarily equivalent to a direct sum of truncated Toeplitz operators.Comment: 15 page

Spatial isomorphisms of algebras of truncated Toeplitz operators

We examine when two maximal abelian algebras in the truncated Toeplitz operators are spatially isomorphic. This builds upon recent work of N. Sedlock, who obtained a complete description of the maximal algebras of truncated Toeplitz operators.Comment: 24 page