Mackey topology on locally convex spaces and on locally quasi-convex groups. Similarities and historical remarks

A counterpart of the Mackey–Arens Theorem for the class of locally quasi-convex topological Abelian groups (LQC-groups) was initiated in Chasco et al. (Stud Math 132(3):257–284, 1999). Several authors have been interested in the problems posed there and have done clarifying contributions, although the main question of that source remains open. Some differences between the Mackey Theory for locally convex spaces and for locally quasi-convex groups, stem from the following fact: The supremum of all compatible locally quasi-convex topologies for a topological abelian group G may not coincide with the topology of uniform convergence on the weak quasi-convex compact subsets of the dual groupG∧. Thus, a substantial part of the classical Mackey–Arens Theorem cannot be generalized to LQC-groups. Furthermore, the mentioned fact gives rise to a grading in the property of “being a Mackey group”, as defined and thoroughly studied in Díaz Nieto and Martín-Peinador (Proceedings in Mathematics and Statistics 80:119–144, 2014). At present it is not known—and this is the main open question—if the supremum of all the compatible locally quasi-convex topologies on a topological group is in fact a compatible topology. In the present paper we do a sort of historical review on the Mackey Theory, and we compare it in the two settings of locally convex spaces and of locally quasi-convex groups. We point out some general questions which are still open, under the name of Problems.

Multivariate orthogonal polynomials and integrable systems

Multivariate orthogonal polynomials in D real dimensions are considered from the perspective of the Cholesky factorization of a moment matrix. The approach allows for the construction of corresponding multivariate orthogonal polynomials, associated second kind functions, Jacobi type matrices and associated three term relations and also Christoffel-Darboux formulae. The multivariate orthogonal polynomials, their second kind functions and the corresponding Christoffel-Darboux kernels are shown to be quasi-determinants as well as Schur complements of bordered truncations of the moment matrix; quasi-tau functions are introduced. It is proven that the second kind functions are multivariate Cauchy transforms of the multivariate orthogonal polynomials. Discrete and continuous deformations of the measure lead to Toda type integrable hierarchy, being the corresponding flows described through Lax and Zakharov-Shabat equations; bilinear equations are found. Varying size matrix nonlinear partial difference and differential equations of the 2D Toda lattice type are shown to be solved by matrix coefficients of the multivariate orthogonal polynomials. The discrete flows, which are shown to be connected with a Gauss-Borel factorization of the Jacobi type matrices and its quasi-determinants, lead to expressions for the multivariate orthogonal polynomials and their second kind functions in terms of shifted quasi-tau matrices, which generalize to the multidimensional realm, those that relate the Baker and adjoint Baker functions to ratios of Miwa shifted tau-functions in the 1D scenario. In this context, the multivariate extension of the elementary Darboux transformation is given in terms of quasi-determinants of matrices built up by the evaluation, at a poised set of nodes lying in an appropriate hyperplane in R^D, of the multivariate orthogonal polynomials. The multivariate Christoffel formula for the iteration of m elementary Darboux transformations is given as a quasi-determinant. It is shown, using congruences in the space of semi-infinite matrices, that the discrete and continuous flows are intimately connected and determine nonlinear partial difference-differential equations that involve only one site in the integrable lattice behaving as a Kadomstev-Petviashvili type system. Finally, a brief discussion of measures with a particular linear isometry invariance and some of its consequences for the corresponding multivariate polynomials is given. In particular, it is shown that the Toda times that preserve the invariance condition lay in a secant variety of the Veronese variety of the fixed point set of the linear isometry.

Measuring the effectiveness of two public policies on the sectors of labor markets and urban infraestructure. Experimental and quasi-experimental evidence from developing countries

La tesis presenta evidencia rigurosa de la efectividad de las políticas públicas utilizando metodologías experimentales y cuasi-experimentales. La tesis comienza con una introducción completa y una revisión rigurosa de las metodologías que se utilizarán en el análisis posterior de los datos. El primer capítulo, "Habilidades personales y habilidades técnicas en programas de formación de jóvenes. Evidencia Experimental de Largo Plazo de República Dominicana ", evalúa el impacto de un programa de empleo de los jóvenes en una serie de variables de interés. El programa ofrece capacitación en las habilidades vocacionales y en las habilidades no cognitivas a jóvenes en riesgo de exclusión social. Cabe destacar que la metodología utilizada para evaluar el programa es un ensayo controlado aleatorio, que proporciona evidencia robusta del efecto causal del programa. Mientras que estudios previos analizaron el impacto de los programas para jóvenes relacionados, ningún estudio anterior había evaluado los efectos de 4 años después de la implementación del programa. Esto representa una contribución importante debido a que las ganancias a corto plazo de varios programas de desarrollo han demostrado no ser sostenida en el tiempo. Esto es también lo que este estudio encuentra para los resultados del mercado de trabajo: mientras que el programa genera una mejora a corto plazo de los resultados de empleo para las mujeres, este efecto se disipa en el largo plazo. Sin embargo, el programa parece conducir a cambios persistentes en las expectativas del mercado de trabajo de las mujeres: las mujeres que asistieron al entrenamiento de informar una visión más optimista de las perspectivas del mercado de trabajo hasta 4 años después del programa...