О Наилучших Методах Восстановления Производных На Соболевских Классах

Магарил-Ильяев, Георгий Георгиевич; Magaril-Il'yaev, Georgii Georgievich; Осипенко, Константин Юрьевич; Osipenko, Konstantin Yur'evich

doi:10.4213/im8182

Cited by 6 publications

(1 citation statement)

References 15 publications

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“…In addition, it was found that the error of the best approximation method can be calculated by the following formula Be the unit ball in the Hardy space (1≤ p <∞) (see the definition of Hardy classes in [2], [3]). We note that the problems of optimal recovery of functions belonging to certain classes and derivatives of functions with respect to their values in a finite number of points have been studied in many papers (see, for example, [1], [4][5][6][7][8][9][10][11][12]). This work is a continuation of [13].…”

Section: Introductionmentioning

confidence: 99%

Linear best method for recovering the second derivatives of Hardy class functions

Ovchintsev

2020

E3S Web Conf.

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The linear best method for approximating the second derivatives of Hardy class functions defined in the unit circle at zero in accordance with the information about their values in a finite number of points forming a regular polygon is found. The paper is divided into three sections. The first contains the necessary concepts and results from the work of K.Yu. Osipenko. It also recalls some results obtained by S. Ya. Havinson and other authors. In the second section, the error of the best method is calculated, and the corresponding extremal functions are written out. The third proves that the linear best approximation method is unique, and its coefficients are calculated.

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Section: Introductionmentioning

confidence: 99%

Linear best method for recovering the second derivatives of Hardy class functions

Ovchintsev

2020

E3S Web Conf.

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Optimal recovery of the derivate from the confined analytic function

Ovchintsev

2024

E3S Web Conf.

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In the article the author finds out the best straight-line method to recover the derivate in zero-point from the confined analytic function determined in the unit circle according to values of the function and values of its derivate in given points creating the regular polygon with zero as the center. The paper consists of three parts. The first part one contains notions and results necessary for the solution of the objective. The second part determines the measure of inaccuracy of the best approximation method and draws out the corresponding extremum function. It is established that the extremum function is the only one to an approximation of the constant multiplier modulo equal to one. The third part calculates coefficients of the best straight-line method of recovery. It is established that the best straight- linear method of recovery is the only one.

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Optimal recovery in weighted spaces with homogeneous weights

Osipenko¹

2022

Sb. Math.

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The paper concerns problems of the recovery of operators from noisy information in weighted -spaces with homogeneous weights. A number of general theorems are proved and applied to problems of the recovery of differential operators from a noisy Fourier transform. In particular, optimal methods are obtained for the recovery of powers of the Laplace operator from a noisy Fourier transform in the -metric. Bibliography: 30 titles.

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О Наилучших Методах Восстановления Производных На Соболевских Классах

Cited by 6 publications

References 15 publications

Linear best method for recovering the second derivatives of Hardy class functions

Linear best method for recovering the second derivatives of Hardy class functions

Optimal recovery of the derivate from the confined analytic function

Optimal recovery in weighted spaces with homogeneous weights

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