719 research outputs found
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 is a positive real linear transformation on a finite dimensional
complex inner product space . The reproducing kernel for the Fock space of
square integrable holomorphic functions on relative to the Gaussian measure
is described
in terms of the holomorphic--antiholomorphic decomposition of the linear
operator . Moreover, if commutes with a conjugation on , then a
restriction mapping to the real vectors in 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, 1985â2003)
and Irminger Sea (IRM-TS, 1983â2013) 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 Âkgâ1 Âyrâ1, 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 Âkgâ1 Âyrâ1 and 32.6 ± 3.4 pmol Âkgâ1 Âyrâ1 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 âUrban 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
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