Yu. N. Subbotin’s Method in the Problem of Extremal Interpolation in the Mean in the Space $$L_p(\mathbb R)$$ with Overlapping Averaging Intervals

IF 0.6 4区数学 Q3 MATHEMATICS

Mathematical Notes Pub Date : 2024-07-15 DOI:10.1134/s0001434624050365

V. T. Shevaldin

引用次数: 0

Abstract

On a uniform grid on the real axis, we study the Yanenko–Stechkin–Subbotin problem of extremal function interpolation in the mean in the space $L_p(\mathbb R)$, $1<p<\infty$, of two-way real sequences with the least value of the norm of a linear formally self-adjoint differential operator ${\mathcal L}_n$ of order $n$ with constant real coefficients. In case of even $n$, the value of the least norm in the space $L_p(\mathbb R)$, $1<p<\infty$, of the extremal interpolant is calculated exactly if the grid step $h$ and the averaging step $h_1$ are related by the inequality $h<h_1\le 2h$.

查看原文本刊更多论文

Yu.苏博廷方法在具有重叠平均区间的 $$L_p(\mathbb R)$$ 空间中平均值的极值插值问题中的应用

摘要在实轴上的均匀网格上，我们研究了Yanenko-Stechkin-Subbotin问题中的极值函数插值在均值空间$L_p(\mathbb R)$,$1<p<\infty$中的双向实序列，其最小值为具有常数实系数的线性形式上自关节微分算子${\mathcal L}_n$的最小值。在偶数$n$的情况下，如果网格步长$h$和平均步长$h_1$通过不等式$h<h_1\le 2h$相关，那么极值插值的空间$L_p(\mathbb R)$,$1<p<\infty$中的最小规范值就可以精确计算出来。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Mathematical Notes 数学-数学

CiteScore

0.90

自引率

16.70%

发文量

179

审稿时长

24 months

期刊介绍： Mathematical Notes is a journal that publishes research papers and review articles in modern algebra, geometry and number theory, functional analysis, logic, set and measure theory, topology, probability and stochastics, differential and noncommutative geometry, operator and group theory, asymptotic and approximation methods, mathematical finance, linear and nonlinear equations, ergodic and spectral theory, operator algebras, and other related theoretical fields. It also presents rigorous results in mathematical physics.