de Branges Spaces and Kreĭn’s Theory of Entire Operators

Luis O. Silva () and Julio H. Toloza ()
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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

Chapter 23 in Operator Theory, 2015, pp 549-580 from Springer

Abstract: 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.

Keywords: Hilbert Space; Entire Function; Functional Model; Symmetric Operator; Wiener Space (search for similar items in EconPapers)
Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-0348-0667-1_4

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DOI: 10.1007/978-3-0348-0667-1_4

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