Spectral cluster bounds for orthonormal systems and oscillatory integral operators in Schatten spaces

We generalize the $L^p$ spectral cluster bounds of Sogge for the Laplace-Beltrami operator on compact Riemannian manifolds to systems of orthonormal functions. The optimality of these new bounds is also discussed. These spectral cluster bounds follow from Schatten-type bounds on oscillatory integral operators.Comment: 30 page

The Stein-Tomas inequality in trace ideals

The goal of this review is to explain some recent results regarding generalizations of the Stein-Tomas (and Strichartz) inequalities to the context of trace ideals (Schatten spaces).Comment: Proceedings of the Laurent Schwartz semina

The role of oil prices in monetary policy rules: evidence from 4 major central banks

Recent movements in oil prices on international markets have generated many comments on the role that oil prices may play for Central Banks of oil-importing countries, oil price shocks being interpreted as supply shocks leading to higher inflation rates and lower economic growth. In this paper, we examine the role played by oil prices in the monetary policy strategy of 4 major Central Banks: the U.S. Federal Reserve, the ECB, the Bank of Canada and the Bank of England. Using an Ordered Probit model, we assess the reaction of each Central Bank to oil price changes and investigate a potential asymmetric response to oil price increases and decreases. Our results suggest that the role of oil price for Central Bankers may be very different depending on the objectives and the strategy of each Central Bank regarding inflation and output stabilization.Oil prices, Monetary policy, Taylor rule, Asymmetry

Maximizers for the Stein-Tomas inequality

We give a necessary and sufficient condition for the precompactness of all optimizing sequences for the Stein-Tomas inequality. In particular, if a well-known conjecture about the optimal constant in the Strichartz inequality is true, we obtain the existence of an optimizer in the Stein-Tomas inequality. Our result is valid in any dimension.Comment: 37 page

Roots Structure and Development of Austrobaileya scandens (Austrobaileyaceae) and Implications for Their Evolution in Angiosperms

Since the resolution of the ANA grade [Amborellales, Nymphaeales, Austrobaileyales] as sister to all other flowering plants, a few comparative studies of root structure have suggested that some of their anatomical traits could be of importance to understanding root evolutionary development and angiosperm phylogeny. However, there is still a paucity of information on root structure and apical meristems (RAMs) in these lineages and especially the sister to all other Austrobaileyales, Austrobaileya scandens. We used microtome sections and bright field, epifluorescence, laser confocal, and scanning electron microscopy to study adventitious root RAMs and tissues of A. scandens. Our results indicate that root structure is relatively simple in A. scandens. The epidermis has a thick cuticle and lacks root hairs. The stele is typically diarch, or some modification thereof, and surrounded by a cortex differentiated into a uniseriate endodermis, a middle region sometimes packed with starch, some oil cells, and colonized by arbuscular mycorrhizal fungi, and a multiseriate exodermis. Secondary growth produced many vessel elements in the secondary xylem and scattered sclerenchymatous fibers in secondary phloem. The absence of distinct patterning within the RAM and between the RAM and derivative differentiating tissues shows that the RAM is open and characterized by common initials. Roots structure and anatomy of A. scandens are thus essentially similar to some previously described in Amborella or Illicium in the ANA grade and many magnoliids, and suggest that the first woody flowering plants likely had an open RAM with common initials. Their functional and evolutionary significance in woody early-diverging and basal lineages of flowering plants and gymnosperms remains unclear, but they are clearly ancestral traits