Related papers: Analysis of astrometric catalogues with vector sph…
In many astronomical works, the structure of vector fields is analyzed, such as the differences in the celestial object coordinates in catalogs or the celestial object velocities, by decomposition into vector spherical harmonics (VSH). This…
We propose an efficient way to test rotational invariance in the cosmological perturbations by use of galaxy correlation functions. In symmetry-breaking cases, the galaxy power spectrum can have extra angular dependence in addition to the…
We present a spectral decomposition technique that separates the contribution of different kinematic components in galaxies from the observed spectrum. This allows to study the kinematics and properties of the stellar populations of the…
Orbital solutions for binary or multiple stellar systems that combine astrometry (e.g., position angles and angular separations) with spectroscopy (radial velocities) have important advantages over astrometric-only or spectroscopic-only…
We present a spectral decomposition technique and its applications to a sample of galaxies hosting large-scale counter-rotating stellar disks. Our spectral decomposition technique allows to separate and measure the kinematics and the…
The combination of ground-based astrometric compilation catalogues, such as the FK5 or the GC, with the results of the ESA Astrometric Satellite HIPPARCOS produces for many thousands of stars proper motions which are significantly more…
Decomposing the field scattered by an object into vector spherical harmonics (VSH) is the prime task when discussing its optical properties on more analytical grounds. Thus far, it was frequently required in the decomposition that the…
The combination of HIPPARCOS measurements with suitable ground-based astrometric data improves significantly the accuracy of the proper motions of bright stars. The comparison of both types of data allows us also to identify and to…
The natural approach to a spectral analysis of data distributed on the sky employs spherical harmonic decomposition. A common problem encountered in practical astronomy is the lack of full sky coverage in the available data. For example,…
In cosmological perturbation theory it is convenient to use the scalar, vector, tensor (SVT) basis as defined according to how these components transform under 3-dimensional rotations. In attempting to solve the fluctuation equations that…
The wave equation for vectors and symmetric tensors in spherical coordinates is studied under the divergence-free constraint. We describe a numerical method, based on the spectral decomposition of vector/tensor components onto spherical…
We study partial fraction decompositions (PFDs) in several variables using tools from commutative algebra. We give criteria for when a rational function with poles on a hyperplane arrangement has a desirable PFD. Our criteria are obtained…
This paper introduces the use of Principal Component Analysis as a method to decompose the waveform catalogues to produce a set of orthonormal basis vectors. We apply this method to a set of supernova waveforms and compare the basis vectors…
The combination of ground-based astrometric compilation catalogues, such as the FK5 or the GC, with the results of the ESA Astrometric Satellite HIPPARCOS produces for many thousands of stars proper motions which are significantly more…
I describe the advantage of using singular value decomposition as a diagnostic tool for exploring the potential and limitations of seismic data. Using stellar models coupled with the expected errors in seismic and complementary data we can…
We present an outline of a new reduction of the Hipparcos astrometric data, the justifications of which are described in the accompanying paper. The emphasis is on those aspects of the data analysis that are fundamentally different from the…
This contribution is intended as a `rough guide' to the Hipparcos Catalogue for the non-expert user. Some general aspects of the use of astrometric data are discussed as well as Hipparcos-specific applications. We discuss when and at what…
Based on the most complete list of the results of an individual comparison of the proper motions for stars of various programs common to the Hipparcos catalog, each of which is an independent realization of the inertial reference frame with…
We propose a number of variational regularisation methods for the estimation and decomposition of motion fields on the $2$-sphere. While motion estimation is based on the optical flow equation, the presented decomposition models are…
The shapelets method for image analysis is based upon the decomposition of localised objects into a series of orthogonal components with convenient mathematical properties. We extend the "Cartesian shapelet" formalism from earlier work, and…