Inner multipliers and Rudin type invariant subspaces

Let $\mathcal{E}$ be a Hilbert space and $H^2_{\mathcal{E}}(\mathbb{D})$ be the $\mathcal{E}$-valued Hardy space over the unit disc $\mathbb{D}$ in $\mathbb{C}$. The well known Beurling-Lax-Halmos theorem states that every shift invariant subspace of $H^2_{\mathcal{E}}(\mathbb{D})$ other than $\{0\}$ has the form $\Theta H^2_{\mathcal{E}_*}(\mathbb{D})$, where $\Theta$ is an operator-valued inner multiplier in $H^\infty_{B(\mathcal{E}_*, \mathcal{E})}(\mathbb{D})$ for some Hilbert space $\mathcal{E}_*$. In this paper we identify $H^2(\mathbb{D}^n)$ with $H^2(\mathbb{D}^{n-1})$-valued Hardy space $H^2_{H^2(\mathbb{D}^{n-1})}(\mathbb{D})$ and classify all such inner multiplier $\Theta \in H^\infty_{\mathcal{B}(H^2(\mathbb{D}^{n-1}))}(\mathbb{D})$ for which $\Theta H^2_{H^2(\mathbb{D}^{n-1})}(\mathbb{D})$ is a Rudin type invariant subspace of $H^2(\mathbb{D}^n)$.Comment: 8 page

Inappropriate Technology

In this paper, we investigate incentives other than altruism that developed countries have in improving technologies specific to developing countries. We propose a simple model of international trade between two regions, in which all individuals have similar preferences over an inferior good and a luxury good. The poor region has a comparative advantage in the production of the inferior good, and the rich in the luxury good. Even when costly adaptation of the technology to the poor region's characteristics is required -- which makes the technology inappropriate for local use -- we show that there are parameter configurations for which the rich region has an incentive to incur this cost. By raising the efficiency of the productive process of the developing region, the developed region can redirect its own productive resources toward the luxury good; it can also gain access to a more diversified set of consumption choices. Indeed, there are cases where the rich region would prefer to improve the poor region's technology for producing the inferior good rather than its own. Such technology transfers can increase the welfare of both regions. We apply our model to the Green Revolution and provide a quantitative assessment of its welfare effects.Technology improvements, Dynamic trade models, Welfare analysis

AR(1) sequence with random coefficients: Regenerative properties and its application

Let $\{X_n\}_{n\ge0}$ be a sequence of real valued random variables such that $X_n=\rho_n X_{n-1}+\epsilon_n,~n=1,2,\ldots$, where $\{(\rho_n,\epsilon_n)\}_{n\ge1}$ are i.i.d. and independent of initial value (possibly random) $X_0$. In this paper it is shown that, under some natural conditions on the distribution of $(\rho_1,\epsilon_1)$, the sequence $\{X_n\}_{n\ge0}$ is regenerative in the sense that it could be broken up into i.i.d. components. Further, when $\rho_1$ and $\epsilon_1$ are independent, we construct a non-parametric strongly consistent estimator of the characteristic functions of $\rho_1$ and $\epsilon_1$

Maximal contractive tuples

Maximality of a contractive tuple of operators is considered. Characterization of a contractive tuple to be maximal is obtained. Notion of maximality of a submodule of Drury-Arveson module on the $d$-dimensional unit ball $\mathbb{B}_d$ is defined. For $d=1$, it is shown that every submodule of the Hardy module over the unit disc is maximal. But for $d\ge 2$ we prove that any homogeneous submodule or submodule generated by polynomials is not maximal. A characterization of a submodule to be maximal is obtained.Comment: 13 page

Globalization and growth in the low Income African countries with the extreme bounds analysis

The relationship between globalization and economic growth, especially in the poorer developing countries, is controversial. Many previous studies have used single globalization indicators such as the ratio of exports plus imports to GDP. This paper uses a comprehensive measure of a globalization of Dreher (2006), which is based on measures of globalization of the economic, social and political sectors. Panel data estimates with data of 21 low income African countries show a small but significant positive permanent growth effects. The sensitivity of this growth effect is examined with the extreme bounds analysis (EBA). Contrary to the findings by Levine and Renelt (1992) that cross country growth relationships are fragile, the effects of globalization and some other determinants of the long run growth rate are found to be robust by EBA.Globalization, Economic growth, Solow model, Africa and Extreme bounds analysis.