相关论文: Flaglets for studying the large-scale structure of…

We summarise the construction of exact axisymmetric scale-discretised wavelets on the sphere and on the ball. The wavelet transform on the ball relies on a novel 3D harmonic transform called the Fourier-Laguerre transform which combines the…

We construct the spin flaglet transform, a wavelet transform to analyze spin signals in three dimensions. Spin flaglets can probe signal content localized simultaneously in space and frequency and, moreover, are separable so that their…

We develop an exact wavelet transform on the three-dimensional ball (i.e. on the solid sphere), which we name the flaglet transform. For this purpose we first construct an exact transform on the radial half-line using damped Laguerre…

We review the Fourier-Laguerre transform, an alternative harmonic analysis on the three-dimensional ball to the usual Fourier-Bessel transform. The Fourier-Laguerre transform exhibits an exact quadrature rule and thus leads to a sampling…

Wavelet analysis is proposed as a new tool for studying the large-scale structure formation of the universe. To reveal its usefulness, the wavelet decomposition of one-dimensional cosmological density fluctuations is performed. In contrast…

Galaxies are arranged in interconnected walls and filaments forming a cosmic web encompassing huge, nearly empty, regions between the structures. Many statistical methods have been proposed in the past in order to describe the galaxy…

We demonstrate the effectiveness of a relatively straightforward analysis of the complex 3D Fourier transform of galaxy coordinates derived from redshift surveys. Numerical demonstrations of this approach are carried out on a volume-limited…

These lectures deal with our current knowledge of the matter distribution in the universe, focusing on how this is studied via the large-scale structure seen in galaxy surveys. We first assemble the necessary basics needed to understand the…

Surveys of galaxy clusters provide a promising method of testing models of structure formation in the universe. Within the context of our standard structure formation scenario, surveys provide measurements of the geometry of the universe…

We suggest a two-dimensional wavelet devised to deduce the large-scale structure of a physical field (e.g., the Galactic magnetic field) from its integrals along straight paths from irregularly spaced data points to a fixed interior point…

We present a new approach to measure the shapes of galaxies, a fundamental task in observational astronomy. This approach is based on the decomposition of a galaxy image into a series of orthogonal basis functions, or `shapelets'. Our…

Future cosmological surveys will provide 3D large scale structure maps with large sky coverage, for which a 3D Spherical Fourier-Bessel (SFB) analysis in spherical coordinates is natural. Wavelets are particularly well-suited to the…

A new generation of interferometric instruments is emerging which aim to use intensity mapping of redshifted $21\,$cm radiation to measure the large-scale structure of the Universe at $z\simeq 1-2$ over wide areas of sky. While these…

In this paper we discuss various possibilities of using X-ray observations to gain information about the large-scale structure of the Universe. After reviewing briefly the current status of these investigations we explore different ways of…

Galaxy redshift surveys are one of the pillars of the current standard cosmological model and remain a key tool in the experimental effort to understand the origin of cosmic acceleration. To this end, the next generation of surveys aim at…

We extend the two-dimensional Cartesian shapelet formalism to d-dimensions. Concentrating on the three-dimensional case, we derive shapelet-based equations for the mass, centroid, root-mean-square radius, and components of the quadrupole…

I review the current status of studies of the large-scale structure of the Universe using redshift surveys of galaxies and clusters of galaxies. I first summarise the advances we have made in our knowledge of the cosmography of the z<0.2…

I review at the non-specialist level recent progress in the study of the large-scale structure of the Universe, covering the following areas: (1) Results from recently completed or ongoing redshift surveys of galaxies and X-ray clusters;…

Here I present results from individual galaxy studies and galaxy surveys in the Local Universe with particular emphasis on the spatially resolved properties of neutral hydrogen gas. The 3D nature of the data allows detailed studies of the…

These are advanced lecture notes covering recent developments in the methodology used to analyse galaxy surveys. The focus is particularly on direct measurements of the galaxy power spectrum although I also discuss its Fourier transform,…