Related papers: Band width estimates of CMC initial data sets

We introduce a weak transversality condition for piecewise C^{1+\alpha} and piecewise hyperbolic maps which admit a C^{1+\alpha} stable distribution. We show good bounds on the essential spectral radius of the associated transfer operators…

Estimators of information theoretic measures such as entropy and mutual information are a basic workhorse for many downstream applications in modern data science. State of the art approaches have been either geometric (nearest neighbor (NN)…

We consider supersymmetric quantum mechanical systems in arbitrary dimensions on curved spaces with nontrivial gauge fields. The square of the Dirac operator serves as Hamiltonian. We derive a relation between the number of supercharges…

We derive bounds on the location of non-embedded eigenvalues of Dirac operators on the half-line with non-Hermitian $L^1$-potentials. The results are sharp in the non-relativistic or weak-coupling limit. In the massless case, the absence of…

This article is concerned with a generalisation of Connes' noncommutative framework. This is achieved by a general study of spectral triples, in particular through an analysis of the role played by the Dirac operator. The Dirac operator is…

It is shown that van Suijlekom's technique of imposing a set of conditions on operator system spectral triples ensures Gromov-Hausdorff convergence of sequences of sets of unital completely positive maps (equipped with the BW-topology which…

We prove local smoothing estimates for the massless Dirac equation with a Coulomb potential in 2 and 3 space dimensions. Our strategy of proof is inspired by a paper of Burq et al. (2003) about Schroedinger and wave equations with…

We discuss resonances for 1D massless Dirac operators with compactly supported potentials on the line. We estimate the sum of the negative power of all resonances in terms of the norm of the potential and the diameter of its support.

We investigate absolutely continuous spectrum of generalized indefinite strings. By following an approach of Deift and Killip, we establish stability of the absolutely continuous spectra of two model examples of generalized indefinite…

We prove stochastic stability of absolutely continuous invariant measures (ACIMs) for piecewise expanding $C^{1+\varepsilon}$ maps of the interval. For maps $\tau$ in the class $\mathcal{T}([0,1]; s, \varepsilon)$, we consider perturbed…

Within the scope of the Planck IDIS (Integrated Data Information System) project we have started to develop the data model for time-ordered data and full-sky maps. The data model is part of the Data Management Component (DMC), a software…

We examine Cosmic Microwave Background (CMB) temperature power spectra from the BOOMERANG, MAXIMA, and DASI experiments. We non-parametrically estimate the true power spectrum with no model assumptions. This is a significant departure from…

We present deep Ka-band ($\nu \approx 33$ GHz) observations of the CMB made with the extended Very Small Array (VSA). This configuration produces a naturally weighted synthesized FWHM beamwidth of $\sim 11$ arcmin which covers an…

Under the assumption that the concordance Lambda cold dark matter (CDM) model is the correct model, we test the cosmic microwave background (CMB) anisotropy data for systematic effects by examining the band pass temperature residuals with…

The spectrum and statistics of the cosmic microwave background radiation (CMBR) are investigated under the hypothesis that scale invariance of the primordial density fluctuations should be promoted to full conformal invariance. As in the…

In this paper, we consider the Cauchy problem of Dirac equations with Chern-Simons-Proca (CSP) gauge field. We investigate global well-posedness and scattering theory for the solutions with small initial data. The main difficulties come…

We present a new, semi-analytic framework for estimating the level of residuals present in CMB maps derived from multi-frequency Cosmic Microwave Background (CMB) data and forecasting their impact on cosmological parameters. The data are…

The frequency spectrum of the cosmic microwave background (CMB) is a relatively untapped source of data which can allow us to peer beyond the surface of last scattering. Small deviations away from a perfect blackbody shape will encode…

Conventional sampling and interpolation commonly rely on discrete measurements. In this paper, we develop a theoretical framework for extrapolation of signals in higher dimensions from knowledge of the continuous waveform on bounded…

We develop a stochastic foundation for bandwidth estimation of networks with random service, where bandwidth availability is expressed in terms of bounding functions with a defined violation probability. Exploiting properties of a…