of One-Dimensional Cosmological Density Fluctuations
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 with the Fourier analysis, the wavelet analysis has advantage of its ability to keep the information for location of local density peaks in addition to that for their scales. The wavelet decomposition of evolving density fluctuations with various initial conditions is examined. By comparing the wavelet analysis with the usual Fourier analysis, we conclude that the wavelet analysis is promising as the data analysis method for the
Abstract : The paper presents a discussion of the structure of hereditary differential systems defined on a Banach space with initial data in the space of p-integrable maps. Both finite and infinite time histories are allowed. A unified approach to Global and Local Cauchy problems on finite or infinite time intervals is presented. An existence theorem for Caratheodory systems and an existence and uniqueness theorem for Lipschitz systems are derived. In both cases continuity of a solution with respect to the initial data is established. (Author)