Scholarlink

This chapter presents a contemporary treatment of Krein’s entire operators with deficiency indices (1, 1) and de Branges’ Hilbert spaces of entire functions. Each of these theories played a central role in the research of both renown mathematicians. Remarkably, entire operators and de Branges spaces are intimately connected, and the interplay between them has had an impact in both spectral theory and the theory of functions. This chapter exhibits the interrelation between Krein’s and de Branges’ theories by means of a functional model and discusses recent developments, giving illustrations of the main objects and applications to the spectral theory of difference and differential operators.

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

De Branges Spaces and Krein’s Theory of Entire Operators

  • 动态工具书词条

  • 发表日期：

    2025年

查看全文
  • Luis O. Silva,
  • Julio H. Toloza

摘要

This chapter presents a contemporary treatment of Krein’s entire operators with deficiency indices (1, 1) and de Branges’ Hilbert spaces of entire functions. Each of these theories played a central role in the research of both renown mathematicians. Remarkably, entire operators and de Branges spaces are intimately connected, and the interplay between them has had an impact in both spectral theory and the theory of functions. This chapter exhibits the interrelation between Krein’s and de Branges’ theories by means of a functional model and discusses recent developments, giving illustrations of the main objects and applications to the spectral theory of difference and differential operators.