Operators, Functions, and Systems: An Easy Reading
Operators, Functions, and Systems: An Easy Reading
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DOI：
10.1090/surv/092
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发表时间：
2002
期刊：
影响因子：
--
通讯作者：
N. Nikolski
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文献类型：
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作者：
N. Nikolski
连同同一作者的配套卷，运算符，函数和系统：一个简单的阅读。第二卷：模型算子和系统，数学调查和专著，第93卷，AMS，2002年，这一独特的工作结合了现代分析及其应用的四个主要课题：A。全纯函数的哈代类，B. Hankel和Toeplitz算子的谱理论，C.线性算子和自由插值的函数模型;无限维系统理论与信号处理。本卷包含A部分和B部分。哈代类的全纯函数被认为是最强大的工具，在复杂的分析为各种应用，开始与傅立叶级数，通过黎曼$\zeta$-功能，所有的方式维纳的理论信号处理。Hankel和Toeplitz算子的谱理论成为调和分析和复分析及其许多应用的支柱。在这本书中，矩问题，Nevanlinna-Pick和Carathodory插值，以及最佳有理逼近被认为是为了说明汉克尔和Toeplitz算子的力量。这本书面向广大读者，从研究生到专业数学家，对算子理论和复变函数感兴趣。这两卷发展了一个基本的方法，同时保留了专家水平，可以应用于高级分析和选定的应用程序。研究生和研究数学家感兴趣的分析。
Together with the companion volume by the same author, Operators, Functions, and Systems: An Easy Reading. Volume 2: Model Operators and Systems, Mathematical Surveys and Monographs, Vol. 93, AMS, 2002, this unique work combines four major topics of modern analysis and its applications: A. Hardy classes of holomorphic functions, B. Spectral theory of Hankel and Toeplitz operators, C. Function models for linear operators and free interpolations, and D. Infinite-dimensional system theory and signal processing. This volume contains Parts A and B. Hardy classes of holomorphic functions is known to be the most powerful tool in complex analysis for a variety of applications, starting with Fourier series, through the Riemann $\zeta$-function, all the way to Wiener's theory of signal processing. Spectral theory of Hankel and Toeplitz operators becomes the supporting pillar for a large part of harmonic and complex analysis and for many of their applications. In this book, moment problems, Nevanlinna-Pick and Carathodory interpolation, and the best rational approximations are considered to illustrate the power of Hankel and Toeplitz operators. The book is geared toward a wide audience of readers, from graduate students to professional mathematicians, interested in operator theory and functions of a complex variable. The two volumes develop an elementary approach while retaining an expert level that can be applied in advanced analysis and selected applications. Readership Graduate students and research mathematicians interested in analysis.