Adjoints of elliptic cone operators

We study the adjointness problem for the closed extensions of a general b-elliptic operator A in x^{-\nu}Diff^m_b(M;E), \nu>0, initially defined as an unbounded operator A:C_c^\infty(M;E)\subset x^\mu L^2_b(M;E)\to x^\mu L^2_b(M;E), \mu \in \R. The case where A is a symmetric semibounded operator is of particular interest, and we give a complete description of the domain of the Friedrichs extension of such an operator.Comment: 40 pages, LaTeX, preliminary versio

Currency Crises: Is Central America Different?

In a recent paper we analyzed the determinants of currency crises in a sample of 30 high and middle income countries (Esquivel and Larrain, 1998). In this work we focus on Central America and analyze whether the determinants of currency crises in this region are different from those identified in our previous work. We conclude that they are not, and show that a small set of macroeconomic variables helps to explain the currency crises that took place in Central America between 1976 and 1996. The results of tests applied here support the empirical approach that attempts to explain currency crises by focusing on the behavior of a few macroeconomic indicators. Part of the interest of this result stems from the fact that the Central American countries had an exchange rate system markedly different from that prevailing in the economies that are usually analyzed in similar studies.

THE IMPACT OF G-3 EXCHANGE RATE VOLATILITY ON DEVELOPING COUNTRIES,

This paper describes G-3 exchange rate volatility and evaluates its impact on developing countries. The paper presents empirical evidence showing that G-3 exchange rate volatility has a robust and significantly negative impact on developing countries’ exports. A one percentage point increase in G-3 exchange rate volatility decreases real exports of developing countries by about 2 per cent, on average. G-3 exchange rate volatility also appears to have a negative influence on foreign direct investment to certain regions, and increases the probability of occurrence of exchange rate crises in developing countries. These results imply that greater stability in the international exchange rate system would help improve trade and foreign direct investment prospects for developing countries – and would help prevent currency crises.

Strong Monogamy of Bipartite and Genuine Multipartite Entanglement: The Gaussian Case

We demonstrate the existence of general constraints on distributed quantum correlations, which impose a trade-off on bipartite and multipartite entanglement at once. For all N-mode Gaussian states under permutation invariance, we establish exactly a monogamy inequality, stronger than the traditional one, that by recursion defines a proper measure of genuine N-partite entanglement. Strong monogamy holds as well for subsystems of arbitrary size, and the emerging multipartite entanglement measure is found to be scale invariant. We unveil its operational connection with the optimal fidelity of continuous variable teleportation networks.Comment: 4 pages, 2 figures. Final version, published in PR

On the closure of elliptic wedge operators

We prove a semi-Fredholm theorem for the minimal extension of elliptic operators on manifolds with wedge singularities and give, under suitable assumptions, a full asymptotic expansion of the trace of the resolvent.Comment: 22 pages, improved expositio

Resolvents of elliptic cone operators

We prove the existence of sectors of minimal growth for general closed extensions of elliptic cone operators under natural ellipticity conditions. This is achieved by the construction of a suitable parametrix and reduction to the boundary. Special attention is devoted to the clarification of the analytic structure of the resolvent.Comment: 46 pages, submitted for publicatio

Trace expansions for elliptic cone operators with stationary domains

We analyze the behavior of the trace of the resolvent of an elliptic cone differential operator as the spectral parameter tends to infinity. The resolvent splits into two components, one associated with the minimal extension of the operator, and another, of finite rank, depending on the particular choice of domain. We give a full asymptotic expansion of the first component and expand the component of finite rank in the case where the domain is stationary. The results make use, and develop further, our previous investigations on the analytic and geometric structure of the resolvent. The analysis of nonstationary domains, considerably more intricate, is pursued elsewhere.Comment: 27 pages. Minor corrections and change of titl

Simple proof of the robustness of Gaussian entanglement in bosonic noisy channels

The extremality of Gaussian states is exploited to show that Gaussian states are the most robust, among all possible bipartite continuous-variable states at fixed energy, against disentanglement due to noisy evolutions in Markovian Gaussian channels involving dissipation and thermal hopping. This proves a conjecture raised recently in [M. Allegra, P. Giorda, and M. G. A. Paris, Phys. Rev. Lett. {\bf 105}, 100503 (2010)], providing a rigorous validation of the conclusions of that work. The problem of identifying continuous variable states with maximum resilience to entanglement damping in more general bosonic open system dynamical evolutions, possibly including correlated noise and non-Markovian effects, remains open.Comment: 3 pages, 1 figure, brief repor

Geometry and spectra of closed extensions of elliptic cone operators

We study the geometry of the set of closed extensions of index 0 of an elliptic cone operator and its model operator in connection with the spectra of the extensions, and give a necessary and sufficient condition for the existence of rays of minimal growth for such operators.Comment: 48 pages, revisited version to appear in Canadian Journal of Mathematic