Уточнены верхние оценки абсолютной постоянной в оценке скорости сходимости в центральной предельной теореме в терминах урезанных моментов. Показано, что абсолютная константа в неравенстве Осипова не превосходит 2.011. Ключевые слова и фразы: центральная предельная теорема, оценка скорости сходимости, абсолютная константа.
We study solvability of boundary value problems for the so-called kinetic operator-differential equations of the form B(t)ut − L(t)u = f , where L(t) and B(t) are families of linear operators defined in a complex Hilbert space E. We do not assume that the operator B is invertible and that the spectrum of the pencil L−λB is included into one of the half-planes Re λ < a or Re λ > a (a ∈ R). Under certain conditions on the above operators, we prove several existence and uniqueness theorems and study smoothness questions in weighted Sobolev spaces for solutions.
Mathematics Subject Classification (2010).Primary 34G10, Secondary 47A50; 74A25; 82C40.
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