On the Life and Work of S. Helgason

This article is a contribution to a Festschrift for S. Helgason. After a biographical sketch, we survey some of his research on several topics in geometric and harmonic analysis during his long and influential career. While not an exhaustive presentation of all facets of his research, for those topics covered we include reference to the current status of these areas.Comment: Final versio

Fock spaces corresponding to positive definite linear transformations

Suppose $A$ is a positive real linear transformation on a finite dimensional complex inner product space $V$. The reproducing kernel for the Fock space of square integrable holomorphic functions on $V$ relative to the Gaussian measure $d\mu_A(z)=\frac {\sqrt {\det A}} {\pi^n}e^{-{\rm Re}} dz$ is described in terms of the holomorphic--antiholomorphic decomposition of the linear operator $A$. Moreover, if $A$ commutes with a conjugation on $V$, then a restriction mapping to the real vectors in $V$ is polarized to obtain a Segal--Bargmann transform, which we also study in the Gaussian-measure setting

The Restriction Principle and Commuting Families of Toeplitz Operators on the Unit Ball

On the unit ball B^n we consider the weighted Bergman spaces H_\lambda and their Toeplitz operators with bounded symbols. It is known from our previous work that if a closed subgroup H of \widetilde{\SU(n,1)} has a multiplicity-free restriction for the holomorphic discrete series of \widetilde{\SU(n,1)}, then the family of Toeplitz operators with H-invariant symbols pairwise commute. In this work we consider the case of maximal abelian subgroups of \widetilde{\SU(n,1)} and provide a detailed proof of the pairwise commutativity of the corresponding Toeplitz operators. To achieve this we explicitly develop the restriction principle for each (conjugacy class of) maximal abelian subgroup and obtain the corresponding Segal-Bargmann transform. In particular, we obtain a multiplicity one result for the restriction of the holomorphic discrete series to all maximal abelian subgroups. We also observe that the Segal-Bargman transform is (up to a unitary transformation) a convolution operator against a function that we write down explicitly for each case. This can be used to obtain the explicit simultaneous diagonalization of Toeplitz operators whose symbols are invariant by one of these maximal abelian subgroups

Contrasting drivers and trends of ocean acidification in the subarctic Atlantic

The processes of warming, anthropogenic CO2 (Canth) accumulation, decreasing pHT (increasing [H+]T; concentration in total scale) and calcium carbonate saturation in the subarctic zone of the North Atlantic are unequivocal in the time-series measurements of the Iceland (IS-TS, 1985–2003) and Irminger Sea (IRM-TS, 1983–2013) stations. Both stations show high rates of Canth accumulation with diferent rates of warming, salinifcation and stratifcation linked to regional circulation and dynamics. At the IS-TS, advected and stratifed waters of Arctic origin drive a strong increase in [H+]T, in the surface layer, which is nearly halved in the deep layer (44.7± 3.6 and 25.5 ± 1.0 pmol ­kg−1 ­yr−1, respectively). In contrast, the weak stratifcation at the IRM-TS allows warming, salinifcation and Canth uptake to reach the deep layer. The acidifcation trends are even stronger in the deep layer than in the surface layer (44.2± 1.0 pmol ­kg−1 ­yr−1 and 32.6 ± 3.4 pmol ­kg−1 ­yr−1 of [H+]T, respectively). The driver analysis detects that warming contributes up to 50% to the increase in [H+]T at the IRM-TS but has a small positive efect on calcium carbonate saturation. The Canth increase is the main driver of the observed acidifcation, but it is partially dampened by the northward advection of water with a relatively low natural CO2 content.PRX18/00312, PID2019-104279GB-C21, UIDB/Multi/04326/2020, CEECINST/00114/2018info:eu-repo/semantics/publishedVersio

Overview of the Nordic Seas CARINA data and salinity measurements

Water column data of carbon and carbon relevant hydrographic and hydrochemical parameters from 188 previously non-publicly available cruises in the Arctic, Atlantic, and Southern Ocean have been retrieved and merged into a new database: CARINA (CARbon IN the Atlantic). The data have been subject to rigorous quality control (QC) in order to ensure highest possible quality and consistency. The data for most of the parameters included were examined in order to quantify systematic biases in the reported values, i.e. secondary quality control. Significant biases have been corrected for in the data products, i.e. the three merged files with measured, calculated and interpolated values for each of the three CARINA regions; the Arctic Mediterranean Seas (AMS), the Atlantic (ATL) and the Southern Ocean (SO). With the adjustments the CARINA database is consistent both internally as well as with GLODAP (Key et al., 2004) and is suitable for accurate assessments of, for example, oceanic carbon inventories and uptake rates and for model validation. The Arctic Mediterranean Seas include the Arctic Ocean and the Nordic Seas, and the quality control was carried out separately in these two areas. This contribution provides an overview of the CARINA data from the Nordic Seas and summarises the findings of the QC of the salinity data. One cruise had salinity data that were of questionable quality, and these have been removed from the data product. An evaluation of the consistency of the quality controlled salinity data suggests that they are consistent to at least ±0.005

Calibration of input parameters in volcanic areas and an enlarged dataset by stochastic finite-fault simulations

The calibration of input parameters is an important task for stochastic finite-fault simulation in volcanic areas, and we manage this in the framework of the European project UPStrat-MaFa. The stochastic simulation method requires the knowledge of fault geometry, source, crust properties of the region, and local site effects. At first, we focused the present study in the pilot test areas: Mt Vesuvius, Campi Flegrei and Mt Etna. Later, we performed two applications for a large magnitude event in the Azores Islands and the South Iceland regions. A general preliminary database of ground-motion records was collected in the test areas, to set up the empirical laws of the ground-motion parameters. The results of the simulations have been compared with observed waveforms and response spectra, to determine the suitability of the parameters used. The results show good agreement between the observed and simulated time histories and response spectra, thus encouraging further efforts towards quantitative high resolution studies on input parameters.Co-financed by the EU - Civil Protection Financial Instrument, in the framework the European project ”Urban disaster Prevention Strategies using MAcroseismic Fields and FAult Sources (Acronym: UPStrat-MAFA, Grant Agreement N. 23031/2011/613486/SUB/A5). http://ec.europa.eu/echo/funding/cp_projects2011_en.htmPublishedLisbon - Portugal4.1. Metodologie sismologiche per l'ingegneria sismicaope

Calibration of input parameters in volcanic areas and an enlarged dataset by stochastic finite-fault simulations

The calibration of input parameters is an important task for stochastic finite-fault simulation in volcanic areas, and we manage this in the framework of the European project UPStrat-MaFa. The stochastic simulation method requires the knowledge of fault geometry, source, crust properties of the region, and local site effects. At first, we focused the present study in the pilot test areas: Mt Vesuvius, Campi Flegrei and Mt Etna. Later, we performed two applications for a large magnitude event in the Azores Islands and the South Iceland regions. A general preliminary database of ground-motion records was collected in the test areas, to set up the empirical laws of the ground-motion parameters. The results of the simulations have been compared with observed waveforms and response spectra, to determine the suitability of the parameters used. The results show good agreement between the observed and simulated time histories and response spectra, thus encouraging further efforts towards quantitative high resolution studies on input parameters

Toeplitz-Based Iterative Image Reconstruction for MRI With Correction for Magnetic Field Inhomogeneity

In some types of magnetic resonance (MR) imaging, particularly functional brain scans, the conventional Fourier model for the measurements is inaccurate. Magnetic field inhomogeneities, which are caused by imperfect main fields and by magnetic susceptibility variations, induce distortions in images that are reconstructed by conventional Fourier methods. These artifacts hamper the use of functional MR imaging (fMRI) in brain regions near air/tissue interfaces. Recently, iterative methods that combine the conjugate gradient (CG) algorithm with nonuniform FFT (NUFFT) operations have been shown to provide considerably improved image quality relative to the conjugate-phase method. However, for non-Cartesian k-space trajectories, each CG-NUFFT iteration requires numerous k-space interpolations; these are operations that are computationally expensive and poorly suited to fast hardware implementations. This paper proposes a faster iterative approach to field-corrected MR image reconstruction based on the CG algorithm and certain Toeplitz matrices. This CG-Toeplitz approach requires k-space interpolations only for the initial iteration; thereafter, only fast Fourier transforms (FFTs) are required. Simulation results show that the proposed CG-Toeplitz approach produces equivalent image quality as the CG-NUFFT method with significantly reduced computation time.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/85903/1/Fessler50.pd