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de Branges Spaces and Kreĭn’s Theory of Entire Operators

In: Operator Theory

Author

Listed:
  • Luis O. Silva

    (Universidad Nacional Autónoma de México, Departamento de Física Matemática, Instituto de Investigaciones en Matemáticas Aplicadas y en Sistemas)

  • Julio H. Toloza

    (Universidad Tecnológica Nacional – Facultad Regional Córdoba, Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), and Centro de Investigación en Informática para la Ingeniería)

Abstract

This work presents a contemporary treatment of Kreĭn’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 work exhibits the interrelation between Kreĭn’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.

Suggested Citation

  • Luis O. Silva & Julio H. Toloza, 2015. "de Branges Spaces and Kreĭn’s Theory of Entire Operators," Springer Books, in: Daniel Alpay (ed.), Operator Theory, edition 127, chapter 23, pages 549-580, Springer.
    • Handle: RePEc:spr:sprchp:978-3-0348-0667-1_4
    DOI: 10.1007/978-3-0348-0667-1_4
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