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Application of Haar functions with cyclic translations in the search for cosmic strings. (English. Russian original) Zbl 1254.83056

Mosc. Univ. Phys. Bull. 66, No. 6, 588-592 (2011); translation from Vest. Mosk. Univ., Ser. III 2011, No. 6, 94-98 (2011).
Summary: Cosmic strings are theoretically predicted linear structures of a cosmological size. The search for cosmic strings in optical and radio observations has been an important area of research in recent years. One of the most effective methods of searching for these objects is the analysis of the anisotropy of cosmic microwave background radiation that could be induced by cosmic strings. For this purpose, the authors propose a method of signal expansion in modified Haar functions with cyclic translations. However, for a system of these functions to be used correctly, one needs to prove its orthonormality and completeness, which is the purpose of this paper.

MSC:

83F05 Relativistic cosmology
83E30 String and superstring theories in gravitational theory
81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
42C40 Nontrigonometric harmonic analysis involving wavelets and other special systems
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