有限希尔伯特变换的不等式和近似:最近结果综述

Australian Journal of Mathematical Analysis and Applications Pub Date : 2018-03-02 DOI:10.20944/PREPRINTS201803.0017.V1

S. Dragomir

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引用次数: 3

摘要

本文综述了作者关于一类函数的有限希尔伯特变换的各种不等式和近似的最新结果，这些函数属于Lipschitzian、单调、凸、有界变分导数或绝对连续等函数。在高阶导数是绝对连续的情况下，给出了更精确的估计。导出了一些带误差界的正交规则。它们可以用于有限希尔伯特变换的数值积分，并且由于误差边界的显式形式，使用户能够先验地预测精度。

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Inequalities and Approximations for the Finite Hilbert Transform: A Survey of Recent Results

In this paper we survey some recent results due to the author concerning various inequalities and approximations for the finite Hilbert transform of a function belonging to several classes of functions, such as: Lipschitzian, monotonic, convex or with the derivative of bounded variation or absolutely continuous. More accurate estimates in the case that the higher order derivatives are absolutely continuous are also provided. Some quadrature rules with error bounds are derived. They can be used in the numerical integration of the finite Hilbert transform and, due to the explicit form of the error bounds, enable the user to predict a priori the accuracy.

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来源期刊

Australian Journal of Mathematical Analysis and Applications Mathematics-Analysis

CiteScore

0.60

自引率

0.00%

发文量

期刊介绍： The Australian Journal of Mathematical Analysis and Applications accepts research papers in all areas of Mathematical Analysis and its numerous applications. Topics covered by the journal include: Real Analysis, Complex Analysis, Inequalities, Numerical analysis, Numerical analysis in abstract spaces, Differential equations, Difference equations, Partial differential equations, Optimization, Fourier analysis, Abstract harmonic analysis, Numerical methods in Fourier analysis, Functional analysis, Operator theory, Miscellaneous applications of functional analysis, Nonlinear functional analysis, Stochastic analysis, Multivariate analysis and all the other fields of their applications. Research in these subjects has been very lively recently, and the interplay between individual areas has enriched them all. The journal seeks high quality original papers of both a research and an expository nature. The purpose of AJMAA is the advancement of mathematics. Editors and referees evaluate submitted papers strictly on the basis of scientific merit, without regard to authors'' nationality, country of residence, institutional affiliation, gender and political views.