Optimal recovery and generalized Carlson inequality for weights with symmetry properties

IF 1.8 2区数学 Q1 MATHEMATICS

Journal of Complexity Pub Date : 2023-11-07 DOI:10.1016/j.jco.2023.101807

K.Yu. Osipenko

引用次数: 0

Abstract

The paper concerns problems of the recovery of operators from noisy information in weighted $L_{q}$ -spaces with homogeneous weights. A number of general theorems are proved and applied to finding exact constants in multidimensional Carlson type inequalities with several weights and problems of the recovery of differential operators from a noisy Fourier transform. In particular, optimal methods are obtained for the recovery of powers of generalized Laplace operators from a noisy Fourier transform in the $L_{p}$ -metric.

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对称权的最优恢复与广义Carlson不等式

研究了齐次权加权lq空间中算子从噪声信息中恢复的问题。证明了若干一般定理，并将其应用于若干权重的多维卡尔森型不等式的精确常数的求取，以及噪声傅里叶变换中微分算子的恢复问题。特别地，得到了从lp度规的噪声傅里叶变换中恢复广义拉普拉斯算子幂的最优方法。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Complexity 工程技术-计算机：理论方法

CiteScore

3.10

自引率

17.60%

发文量

审稿时长

>12 weeks

期刊介绍： The multidisciplinary Journal of Complexity publishes original research papers that contain substantial mathematical results on complexity as broadly conceived. Outstanding review papers will also be published. In the area of computational complexity, the focus is on complexity over the reals, with the emphasis on lower bounds and optimal algorithms. The Journal of Complexity also publishes articles that provide major new algorithms or make important progress on upper bounds. Other models of computation, such as the Turing machine model, are also of interest. Computational complexity results in a wide variety of areas are solicited. Areas Include: • Approximation theory • Biomedical computing • Compressed computing and sensing • Computational finance • Computational number theory • Computational stochastics • Control theory • Cryptography • Design of experiments • Differential equations • Discrete problems • Distributed and parallel computation • High and infinite-dimensional problems • Information-based complexity • Inverse and ill-posed problems • Machine learning • Markov chain Monte Carlo • Monte Carlo and quasi-Monte Carlo • Multivariate integration and approximation • Noisy data • Nonlinear and algebraic equations • Numerical analysis • Operator equations • Optimization • Quantum computing • Scientific computation • Tractability of multivariate problems • Vision and image understanding.