Lectures on Analytic Function Spaces and Their Applications
暫譯: 解析函數空間及其應用講座

Mashreghi, Javad

Lectures on Analytic Function Spaces and Their Applications
  • 出版商: Springer
  • 出版日期: 2024-10-14
  • 售價: $5,260
  • 貴賓價: 9.5 折 $4,997
  • 語言: 英文
  • 頁數: 416
  • 裝訂: Quality Paper - also called trade paper
  • ISBN: 3031335740
  • ISBN-13: 9783031335747
  • 相關分類: 數學

    • 海外代購書籍(需單獨結帳)

相關主題

商品描述

The focus program on Analytic Function Spaces and their Applications took place at Fields Institute from July 1st to December 31st, 2021. Hilbert spaces of analytic functions form one of the pillars of complex analysis. These spaces have a rich structure and for more than a century have been studied by many prominent mathematicians. They have essential applications in other fields of mathematics and engineering. The most important Hilbert space of analytic functions is the Hardy class H2. However, its close cousins--the Bergman space A2, the Dirichlet space D, the model subspaces Kt, and the de Branges-Rovnyak spaces H(b)--have also garnered attention in recent decades. Leading experts on function spaces gathered and discussed new achievements and future venues of research on analytic function spaces, their operators, and their applications in other domains.
With over 250 hours of lectures by prominent mathematicians, the program spanned a wide variety of topics. Moreexplicitly, there were courses and workshops on Interpolation and Sampling, Riesz Bases, Frames and Signal Processing, Bounded Mean Oscillation, de Branges-Rovnyak Spaces, Blaschke Products and Inner Functions, and Convergence of Scattering Data and Non-linear Fourier Transform, among others. At the end of each week, there was a high-profile colloquium talk on the current topic. The program also contained two advanced courses on Schramm Loewner Evolution and Lattice Models and Reproducing Kernel Hilbert Space of Analytic Functions.
This volume features the courses given on Hardy Spaces, Dirichlet Spaces, Bergman Spaces, Model Spaces, Operators on Function Spaces, Truncated Toeplitz Operators, Semigroups of weighted composition operators on spaces of holomorphic functions, the Corona Problem, Non-commutative Function Theory, and Drury-Arveson Space. This volume is a valuable resource for researchers interested in analytic function spaces.

商品描述(中文翻譯)

聚焦於解析函數空間及其應用的計畫於2021年7月1日至12月31日在Fields Institute舉行。解析函數的希爾伯特空間是複分析的基石之一。這些空間具有豐富的結構，並且在過去一個世紀中受到許多著名數學家的研究。它們在數學和工程的其他領域中具有重要的應用。最重要的解析函數希爾伯特空間是Hardy類H2。然而，其近親——Bergman空間A2、Dirichlet空間D、模型子空間Kt，以及de Branges-Rovnyak空間H(b)——在近幾十年來也引起了關注。功能空間的領先專家聚集在一起，討論解析函數空間及其運算子在其他領域的應用的新成就和未來研究方向。

該計畫包含超過250小時的著名數學家講座，涵蓋了各種主題。更具體地說，課程和研討會包括插值與取樣、Riesz基底、框架與信號處理、有界均值振盪、de Branges-Rovnyak空間、Blaschke乘積與內部函數，以及散射數據的收斂與非線性傅立葉變換等。在每週結束時，會有一場關於當前主題的高端座談會演講。該計畫還包含兩門關於Schramm Loewner演化和格模型及解析函數的再生核希爾伯特空間的高級課程。

本卷特別介紹了有關Hardy空間、Dirichlet空間、Bergman空間、模型空間、函數空間上的運算子、截斷Toeplitz運算子、在全純函數空間上的加權組合運算子半群、Corona問題、非交換函數理論以及Drury-Arveson空間的課程。本卷對於對解析函數空間感興趣的研究人員來說，是一個寶貴的資源。

作者簡介

Javad Mashreghi is a mathematician and author working in fields of function space theory, functional analysis and complex analysis. He is a professeur titulaire at Laval University and was recently the 35th President of the Canadian Mathematical Society (2020-2022). He is immensely involved in various aspects of North America's mathematical community, having served on numerous editorial, administrative and selection committees all across Canada and the U.S. (CMS, AMS, Fields Institute, CRM, AARMS, NSERC, FQRNT, NSF). He is the editor-in-chief of the Canadian Mathematical Bulletin (2020-2025) and Concrete Operators (2018-2022), and the Analysis Section Editor of the Proceedings of the American Mathematical Society (2020-2027). Among his awards and distinctions, there are the IEEE Prize Paper Award, 2021, the Fellow of the Canadian Mathematical Society, 2019, the Khwarizmi International Award, Research Prize of IROST, 2009, which he declined, the G. de B. Robinson Award, 2004. As for publications, he has more than 120 articles, 12 books (e.g., published by Cambridge, Oxford, AMS and Springer) and 10 conference proceedings.

作者簡介(中文翻譯)

Javad Mashreghi 是一位數學家和作者，專注於函數空間理論、泛函分析和複變分析等領域。他是拉瓦爾大學的教授，並且最近擔任了加拿大數學學會的第35任會長（2020-2022）。他在北美的數學社群中非常活躍，曾在加拿大和美國的多個編輯、行政和選拔委員會中任職（如CMS、AMS、Fields Institute、CRM、AARMS、NSERC、FQRNT、NSF）。他是《加拿大數學公報》（2020-2025）和《具體算子》（2018-2022）的主編，以及《美國數學學會會議錄》的分析部分編輯（2020-2027）。在他的獎項和榮譽中，包括2021年的IEEE獎論文獎、2019年的加拿大數學學會院士、2009年拒絕的Khwarizmi國際獎、以及2004年的G. de B. Robinson獎。至於出版物，他擁有超過120篇文章、12本書（例如由劍橋、牛津、AMS和施普林格出版）和10篇會議論文集。

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