Integral Representations for the Class of Generalized Metaplectic Operators

This article gives explicit integral formulas for the so-called generalized metaplectic operators, i.e. Fourier integral operators (FIOs) of Schr\"odinger type, having a symplectic matrix as canonical transformation. These integrals are over specific linear subspaces of R^d, related to the d x d upper left-hand side submatrix of the underlying 2d x 2d symplectic matrix. The arguments use the integral representations for the classical metaplectic operators obtained by Morsche and Oonincx in a previous paper, algebraic properties of symplectic matrices and time-frequency tools. As an application, we give a specific integral representation for solutions to the Cauchy problem of Schr\"odinger equations with bounded perturbations for every instant time t in R, even in the so-called caustic points.Comment: 19 pages in Journal of Fourier Analysis and Applications, 201

Weak-Type estimates for the metaplectic representation restricted to the shearing and Dilation subgroup of SL(2, ℝ)

We consider the subgroup G of SL(2, ℝ) consisting of shearing and dilations, and we study the decay at infinity of the matrix coefficients of the metaplectic representation restricted to G. We prove weak-type estimates for such coefficients, which are uniform for functions in the modulation space M 1 . This work represents a continuation of a project aiming at studying weak-type and Strichartz estimates for unitary representations of non-compact Lie groups

The Effect of Zonally Asymmetric Ozone Heating on the Northern Hemisphere Winter Polar Stratosphere

[1] Previous modeling studies have found significant differences in winter extratropical stratospheric temperatures depending on the presence or absence of zonally asymmetric ozone heating (ZAOH), yet the physical mechanism causing these differences has not been fully explained. The present study describes the effect of ZAOH on the dynamics of the Northern Hemisphere extratropical stratosphere using an ensemble of free-running atmospheric general circulation model simulations over the 1 December - 31 March period. We find that the simulations including ZAOH produce a significantly warmer and weaker stratospheric polar vortex in mid-February due to more frequent major stratospheric sudden warmings compared to the simulations using only zonal mean ozone heating. This is due to regions of enhanced Eliassen-Palm flux convergence found in the region between 40°N–70°N latitude and 10–0.05 hPa. These results are consistent with changes in the propagation of planetary waves in the presence of ZAOH predicted by an ozone-modified refractive index

Effect of doping and oxygen vacancies on the octahedral tilt transitions in the BaCeO3 perovskite

We present a systematic study of the effect of Y doping and hydration level on the structural transformations of BaCeO3 based on anelastic spectroscopy experiments. The temperature of the intermediate transformation between rhombohedral and orthorhombic Imma phases rises with increasing the molar fraction x of Y roughly as (500 K)x in the hydrated state, and is depressed of more than twice that amount after complete dehydration. This is explained in terms of the effect of doping on the average (Ce/Y)-O and Ba-O bond lengths, and of lattice relaxation from O vacancies. The different behavior of the transition to the lower temperature Pnma orthorhombic phase is tentatively explained in terms of progressive flattening of the effective shape of the OH ion and ordering of the O vacancies during cooling.Comment: 8 pages, 5 figure