C. Pope'
title: Eigenmode Analysis of Galaxy Distributions in Redshift Space
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 Introduction \[sec1\] 
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The large-scale structure (LSS) of the universe offers invaluable information on cosmology. The clustering pattern of galaxies reflects what the primordial universe looks like and how the universe evolves. In contrast to the observations of the cosmic microwave background (CMB), in which only information from photons emitted at a fixed redshift $z_{\rm dec} \simeq 1090$ are observed, the observations of the LSS provide information from photons emitted at various redshifts $z {\lower.5ex\hbox{{$\; \buildrel < \over \sim \;$}}}5$. Therefore, while the CMB primarily tells us the state of the early universe, the LSS shows us that of the present universe and its recent evolution. Detailed analysis of the LSS is extremely important in order to obtain a consistent picture of the evolving universe.

The spatial distribution of galaxies has particular importance in cosmology. Traditionally the power spectrum, or the correlation function is computed from galaxy distributions and is compared with theoretical predictions. Strictly speaking, the power spectrum and the correlation function are properly evaluated only when the sample is homogeneous. In a real-world observation, homogeneous sampling of galaxies is not possible. The sampling density varies with 