Optimal recovery of values of functions and their derivatives from inaccurate data on the Fourier transform

Abstract

This paper presents the results of searches for anisotropy in the arrival directions of ultra-high-energy cosmic rays (CRs) detected with the Yakutsk Array during the 1974-2008 observational period as well as searches in available data from other giant extensive air shower arrays working at present. A method of analysis based on a comparison of the minimum width of distributions in equatorial coordinates is used. As a result, a hypothesis of isotropy in arrival directions is rejected at the 99.5% significance level. The observed decrease in the minimum width of the distribution can be explained by the presence of CR sources in energy intervals and sky regions according to recent indications inferred from data of the Yakutsk Array and Telescope Array experiments.

APPROXIMATION OF DIFFERENTIATION OPERATORS BY BOUNDED LINEAR OPERATORS IN LEBESGUE SPACES ON THE AXIS AND RELATED PROBLEMS IN THE SPACES OF \((p,q)\)-MULTIPLIERS AND THEIR PREDUAL SPACES

“…Inequalities of type (3.40) containing the norms of intermediate and highest derivatives and the norm of the Fourier transform of functions, with norm parameters different from (3.40), also arose in the studies by Magaril-Il'yaev and Osipenko of extremal problems of recovering functions from information about their spectrum [39,40].…”

Оптимальное Восстановление Линейных Операторов В Неевклидовых Метриках

“…Имеется определенная связь между погрешностями приближения в этих задачах, а также между соответствующими экстремальными операторами, что часто позволяет решить одновременно эти задачи (см. [18], [19]). В свою очередь обе эти задачи в частных случаях приводят к точным неравенствам для производных -этой теме посвящено большое число работ.…”