Examples of Coorbit Spaces for Dual Pairs

In this paper we summarize and give examples of a generalization of the coorbit space theory initiated in the 1980's by H.G. Feichtinger and K.H. Gr\"ochenig. Coorbit theory has been a powerful tool in characterizing Banach spaces of distributions with the use of integrable representations of locally compact groups. Examples are a wavelet characterization of the Besov spaces and a characterization of some Bergman spaces by the discrete series representation of $\mathrm{SL}_2(\mathbb{R})$. We present examples of Banach spaces which could not be covered by the previous theory, and we also provide atomic decompositions for an example related to a non-integrable representation

Coorbit Spaces for Dual Pairs

In this paper we present an abstract framework for construction of Banach spaces of distributions from group representations. This generalizes the theory of coorbit spaces initiated by H.G. Feichtinger and K. Gr\"ochenig in the 1980's. Spaces that can be described by this new technique include the whole Banach-scale of Bergman spaces on the unit disc. For these Bergman spaces we show that atomic decompositions can be constructed through sampling. We further present a wavelet characterization of Besov spaces on the forward light cone

Weathering the financial storm: The importance of fundamentals and flexibility

The recent global financial tsunami has had economic consequences that have not been witnessed since the Great Depression. But while some countries suffered a particularly large contraction in economic activity on top of a system-wide banking and currency collapse, others came off relatively lightly. In this paper, we attempt to explain this cross-country variation in post-crisis experience, using a wide variety of pre-crisis explanatory variables in a sample of 46 medium-to-high income countries. We find that domestic macroeconomic imbalances and vulnerabilities were crucial for determining the incidence and severity of the crisis. In particular, we find that the pre-crisis rate of inflation captures factors which are important in explaining the post-crisis experience. Our results also suggest an important role for financial factors. In particular, we find that large banking systems tended to be associated with a deeper and more protracted consumption contraction and a higher risk of a systemic banking or currency crisis. Our results suggest that greater exchange rate flexibility coincided with a smaller and shorter contraction, but at the same time increased the risk of a banking and currency crisis. Countries with exchange rate pegs outside EMU were hit particularly hard, while inflation targeting seemed to mitigate the crisis. Finally, we find some evidence suggesting a role for international real linkages and institutional factors. Our key results are robust to various alterations in the empirical setup and we are able to explain a significant share of the cross-country variation in the depth and duration of the crisis and provide quite sharp predictions of the incidence of banking and currency crises. This suggests that country-specific initial conditions played an important role in determining the economic impact of the crisis and, in particular, that countries with sound fundamentals and flexible economic frameworks were better able to weather the financial storm.

Extensions of real bounded symmetric domains

For a real bounded symmetric domain, G/K, we construct various natural enlargements to which several aspects of harmonic analysis on G/K and G have extensions. Our starting point is the realization of G/K as a totally real submanifold in a bounded domain G_h/K_h. We describe the boundary orbits and relate them to the boundary orbits of G_h/K_h. We relate the crown and the split-holomorphic crown of G/K to the crown \Xi_h of G_h/K_h. We identify an extension of a representation of K to a larger group L_c and use that to extend sections of vector bundles over the Borel compactification of G/K to its closure. Also, we show there is an analytic extension of K-finite matrix coefficients of G to a specific Matsuki cycle space

Ramanujan\u27s Master Theorem for the Hypergeometric Fourier Transform Associated with Root Systems

Ramanujan\u27s Master theorem states that, under suitable conditions, the Mellin transform of an alternating power series provides an interpolation formula for the coefficients of this series. Ramanujan applied this theorem to compute several definite integrals and power series, which explains why it is referred to as the Master Theorem . In this paper we prove an analogue of Ramanujan\u27s Master theorem for the hypergeometric Fourier transform associated with root systems. This theorem generalizes to arbitrary positive multiplicity functions the results previously proven by the same authors for the spherical Fourier transform on semisimple Riemannian symmetric spaces. © 2013 Springer Science+Business Media New York

SYMMETRIC SPACES WITH DISSECTING INVOLUTIONS

An involutive diffeomorphism σ of a connected smooth manifold M is called dissecting if the complement of its fixed point set is not connected. Dissecting involutions on a complete Riemannian manifold are closely related to constructive quantum field theory through the work of Dimock and Jaffe/Ritter on the construction of reflection positive Hilbert spaces. In this article we classify all pairs (M, σ), where M is an irreducible connected symmetric space, not necessarily Riemannian, and σ is a dissecting involutive automorphism. In particular, we show that the only irreducible, connected and simply connected Riemannian symmetric spaces with dissecting isometric involutions are Sn and ℍn, where the corresponding fixed point spaces are Sn−1 and ℍn − 1, respectively

METEOROLOGICAL AND HYDROLOGICAL MODELING OF AN EXTREME PRECIPITATION EVENT IN S–ICELAND

The atmospheric conditions and surface runoff during an event of extreme precipitation have been simulated using numerical weather and hydrological runoff models. The results are compared to the available observations, indicating that the simulations are quite successful in reproducing the event. In the atmospheric simulations, there are very large orographic gradients in precipitation, but no direct observations to verify these gradients. The increase in runoff provides however an indirect validation and the quality of the results are such that numerically simulated precipitation will be used in future hydrological studies in the region. These studies are of great importance to improve flood prediction for the area and for the creation of design floods for various hydropower plants, reservoirs and diversion structures within the river basin

QMM A Quarterly Macroeconomic Model of the Icelandic Economy

This paper documents and describes the new Quarterly Macroeconomi Model of the Central Bank of Iceland (qmm). qmm and the underlying quar terly database have been under construction since 2001 at the Research and Forecasting Division of the Economics Department at the Bank. qmm is used by the Bank for forecasting and various policy simulations and therefore play a key role as an organisational framework for viewing the medium-term futur when formulating monetary policy at the Bank. This paper is mainly focused on the short and medium-term properties of qmm. Analysis of the steady state properties of the model are currently under way and will be reported in a separate paper in the near future.

QMM. A Quarterly Macroeconomic Model of the Icelandic Economy

This paper documents and describes Version 2.0 of the Quarterly Macroeconomic Model of the Central Bank of Iceland (QMM). QMM and the underlying quarterly database have been under construction since 2001 at the Research and Forecasting Division of the Economics Department at the Bank and was first implemented in the forecasting round for the Monetary Bulletin 2006.1 in March 2006. QMM is used by the Bank for forecasting and various policy simulations and therefore plays a key role as an organisational framework for viewing the medium-term future when formulating monetary policy at the Bank. This paper is mainly focused on the short and medium-term properties of QMM. Steady state properties of the model are documented in a paper by Daníelsson (2009).