Оптимальное восстановление функций по неточно заданному преобразованию Радона на классах, задаваемых степенью оператора Лапласа

We consider the problem of optimal recovery of function in Schwartz space from inaccurate data (in the mean square metric) on it’s Radon transform. We present explicit expressions for the error of optimal recovery and a set of optimal methods. As a consequence we prove one inequality for functions in Schwartz space.В работе рассматривается задача оптимального восстановления функции из пространства Шварца по неточно заданному (в средне квадратичной метрике) преобразованию Радона. Получены явные выражения для погрешности оптимального восстановления и семейства оптимальных методов. В качестве следствия приведено одно неравенство для функций из пространства Шварца

Optimal recovery of harmonic functions in the ball from inaccurate information on the Radon transform

We consider the problem of the optimal recovery of harmonic functions in the ball from inaccurate information on the Radon transform. Presented are the error of the optimal recovery and the set of optimal methods for which this error is attained. © 2015, Pleiades Publishing, Ltd

On a problem of optimal recovery and Kolmogorov type inequalities on an interval

We consider an optimal recovery problem for the k-th derivative of the function on an interval from the information on the function itself, given in the mean square metric. As a consequence of the solution we prove one Kolmogorov type inequality for derivatives on an interval and demonstrate that the constant in this inequality can be reduced by considering particular subsets of the function class. © 2014 Published by Elsevier Inc

On a problem of optimal recovery and Kolmogorov type inequalities on an interval

We consider an optimal recovery problem for the k-th derivative of the function on an interval from the information on the function itself, given in the mean square metric. As a consequence of the solution we prove one Kolmogorov type inequality for derivatives on an interval and demonstrate that the constant in this inequality can be reduced by considering particular subsets of the function class. © 2014 Published by Elsevier Inc

Optimal recovery of harmonic functions in the ball from inaccurate information on the Radon transform

We consider the problem of the optimal recovery of harmonic functions in the ball from inaccurate information on the Radon transform. Presented are the error of the optimal recovery and the set of optimal methods for which this error is attained. © 2015, Pleiades Publishing, Ltd