Extremal Problems of Analysis and Applications
暫譯: 分析的極值問題及其應用

Babenko, Vladyslav, Kofanov, Volodymyr, Kogut, Peter

Extremal Problems of Analysis and Applications
  • 出版商: Springer
  • 出版日期: 2025-09-27
  • 售價: $2,180
  • 貴賓價: 9.5 折 $2,071
  • 語言: 英文
  • 頁數: 205
  • 裝訂: Hardcover - also called cloth, retail trade, or trade
  • ISBN: 3031947312
  • ISBN-13: 9783031947315
  • 相關分類: 工程數學 Engineering-mathematics

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商品描述

This book presents solutions to various extremal problems in analysis and provides mathematical tools that can be used to solve complex problems in different areas of fundamental and applied science. These problems are not just theoretical, but they have practical applications in various fields including optimization and image processing. The book includes an in-depth exploration of Ostrowski type inequalities, covering their applications to operator theory, inequalities for derivatives, and optimization of cubature formulae. The authors also provide a comprehensive treatment of the Bojanov-Naidenov and Erdos problems and investigate their solutions for various function classes including differentiable functions, trigonometric polynomials, and splines. Additionally, the book explores sharp Remez type inequalities. These inequalities are examined in different metrics for various function classes including trigonometric polynomials and splines. The authors also include innovative research in image processing, focusing on the restoration of noise-corrupted optical images with simultaneous contrast enhancement and a variational approach to simultaneous fusion and denoising of color images with different spatial resolutions. This book is a valuable resource for researchers and graduate students in approximation theory, numerical analysis, and image processing.

商品描述(中文翻譯)

本書提供了分析中各種極值問題的解決方案，並提供可用於解決基礎科學和應用科學不同領域複雜問題的數學工具。這些問題不僅僅是理論上的，還在優化和影像處理等各個領域具有實際應用。本書深入探討了Ostrowski型不等式，涵蓋了其在算子理論、導數不等式和立方公式優化中的應用。作者還全面處理了Bojanov-Naidenov和Erdos問題，並研究了這些問題在不同函數類別中的解，包括可微函數、三角多項式和樣條函數。此外，本書探討了尖銳的Remez型不等式，這些不等式在不同度量下針對各種函數類別進行了檢視，包括三角多項式和樣條函數。作者還包括了影像處理方面的創新研究，專注於噪聲污染光學影像的恢復，並同時進行對比度增強，以及針對不同空間解析度的彩色影像進行同時融合和去噪的變分方法。本書是近似理論、數值分析和影像處理領域研究人員和研究生的重要資源。

作者簡介

Vladyslav Babenko, Ph. D., Habilitated Doctor in Mathematics, is Professor in the Department of Mathematical Analysis and Optimization at Oles Honchar Dnipro National University, where his teaching focuses on functional analysis and theory of Functions of real and complex variables. His research interests include areas of analysis and approximation theory. Dr. Babenko has over 450 journal publications in mathematical sciences and has published four books.

Vladimir Kofanov, Ph. D., Habilitated Doctor in Mathematics, is Professor in the Department of Mathematical Analysis and Optimization at Oles Honchar Dnipro National University, where his teaching focuses on functional analysis and theory of functions of real and complex variables. Hi research interests include different areas of theory of inequalities for derivatives of differentiable functions as well as polynomials and splines and their applications in approximation theory. Dr. Kofanov has over 200 journal publications in mathematical sciences and has published three books.

Peter Kogut, Ph. D., Habilitated Doctor in Mathematics, is Professor in the Department of Mathematical Analysis and Optimization at Oles Honchar Dnipro National University, where his teaching focuses on variational methods in mathematical physics, optimal control theory for distributed systems, and nonlinear functional analysis. His research interests include the different areas of optimization theory, optimal control problems for PDEs, image processing, asymptotic analysis, optimization in partially ordered spaces, and homogenization theory. He has over 200 journal publications in mathematical sciences and two books.

Oleg Kovalenko, Ph. D., Habilitated Doctor in Mathematics, is Professor in the Department of Mathematical Analysis and Optimization at Oles Honchar Dnipro National University, where his teaching focuses on mathematical analysis, complex analysis, and numeric Methods. He conducts research in the following areas: extremal problems in approximation theory for numeric and non-numeric functions, inequalities for derivatives, and optimal recovery problems.

Nataliia Parfinovych, Ph. D., Habilitated Doctor in Mathematics, is Head of the Department of Mathematical Analysis and Optimization at Oles Honchar Dnipro National University, where her teaching focuses on mathematical analysis, approximation theory, harmonic analysis and its application, and mathematics teaching methods. She conducts research and has achieved notable results in the following areas: extremal problems in approximation theory, approximation of individual functions and functional classes by splines and their analogues, investigation of internal properties of approximating aggregates, inequalities for norms of fractional and integer derivatives, approximation of unbounded operators by bounded ones, and optimal recovery of operators on inaccurate information. She is the Editor-in-Chief of the scientific journal Research in Mathematics.

作者簡介(中文翻譯)

Vladyslav Babenko 博士，數學的合格博士，是烏克蘭奧列斯·霍恩查爾·第聶伯國立大學數學分析與優化系的教授，他的教學專注於泛函分析及實變與複變函數理論。他的研究興趣包括分析學和逼近理論等領域。Babenko 博士在數學科學領域擁有超過 450 篇期刊發表，並出版了四本書籍。

Vladimir Kofanov 博士，數學的合格博士，是烏克蘭奧列斯·霍恩查爾·第聶伯國立大學數學分析與優化系的教授，他的教學專注於泛函分析及實變與複變函數理論。他的研究興趣包括可微函數的導數不等式理論、以及多項式和樣條函數及其在逼近理論中的應用。Kofanov 博士在數學科學領域擁有超過 200 篇期刊發表，並出版了三本書籍。

Peter Kogut 博士，數學的合格博士，是烏克蘭奧列斯·霍恩查爾·第聶伯國立大學數學分析與優化系的教授，他的教學專注於數學物理中的變分法、分佈系統的最優控制理論以及非線性泛函分析。他的研究興趣包括優化理論的不同領域、偏微分方程的最優控制問題、影像處理、漸近分析、在部分有序空間中的優化以及均質化理論。他在數學科學領域擁有超過 200 篇期刊發表和兩本書籍。

Oleg Kovalenko 博士，數學的合格博士，是烏克蘭奧列斯·霍恩查爾·第聶伯國立大學數學分析與優化系的教授，他的教學專注於數學分析、複分析和數值方法。他的研究領域包括：數值和非數值函數的逼近理論中的極值問題、導數的不等式以及最優恢復問題。

Nataliia Parfinovych 博士，數學的合格博士，是烏克蘭奧列斯·霍恩查爾·第聶伯國立大學數學分析與優化系的系主任，她的教學專注於數學分析、逼近理論、調和分析及其應用，以及數學教學方法。她在以下領域進行研究並取得顯著成果：逼近理論中的極值問題、通過樣條及其類似物對個別函數和泛函類的逼近、對逼近聚合物內部特性的研究、分數和整數導數的範數不等式、無界算子通過有界算子的逼近，以及在不準確信息下的算子最優恢復。她是科學期刊《數學研究》的主編。

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