Derivative of functions in de branges and dirichlet spaces

de branges 和 Dirichlet 空间中函数的导数

• 批准号: 251135-2007
• 负责人: Mashreghi, Javad
• 金额: $ 0.73万
• 依托单位: Université Laval
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2007
• 资助国家: 加拿大
• 起止时间: 2007-01-01 至 2008-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=361719
• 关键词: Derivative; functions; de; branges; dirichlet

Complex analysis and harmonic analysis are two old and closely related branches of classical analysis. Moreover, they have many applications in applied sciences and engineering. For example it is rather impossible to find an engineer who has not heard of Fourier analysis.Model subspaces of the Hardy space H2 was the main theme of my previous NSERC research project. No doubt this subject has a variety of applications in pure and applied sciences, e.g. operator theory, control engineering and quantum physics. V. Havin and I were awarded the G. de B. Robinson prize of the Canadian Mathematical Society for publishing two long papers in the Canadian Mathematical Journal on this subject.De Branges spaces are a generalization of model subspaces. Dirichlet spaces are another family of spaces of analytic functions with close relations to Hardy spaces. Studying these spaces is a new and highly active area of research with many interesting open questions. In particular, we would like to explore the application of these spaces in control theory, a subject that has not been touched yet. To do this we have to enrich the subject itself and obtain some necessary tools. In this project we study the derivative of functions in these spaces, their invariant subspaces under the shift operators and their zero sets.

复分析与调和分析是经典分析中两个古老而又密切相关的分支。此外，它们在应用科学和工程中有许多应用。例如，这是相当不可能找到一个工程师谁没有听说过傅立叶分析。模型子空间的哈代空间H2是我以前的NSERC研究项目的主题。毫无疑问，这门学科在纯科学和应用科学中有着广泛的应用，例如算子理论、控制工程和量子物理。哈文和我被授予G。de B.罗宾逊奖的加拿大数学学会发表两篇长论文在加拿大数学杂志上就这个问题。德布兰日空间是一个推广的模型子空间。狄利克雷空间是另一类与哈代空间有密切关系的解析函数空间。研究这些空间是一个新的和高度活跃的研究领域，有许多有趣的开放问题。特别是，我们想探索这些空间在控制理论中的应用，这是一个尚未触及的主题。要做到这一点，我们必须丰富学科本身，并获得一些必要的工具。在这个项目中，我们研究了这些空间中函数的导数，它们在移位算子下的不变子空间以及它们的零点集。