Reproducing Kernel Kreĭn Spaces

Aurelian Gheondea ()
Additional contact information
Aurelian Gheondea: Bilkent University, Department of Mathematics and Institutul de Matematicăal Academiei

Chapter 14 in Operator Theory, 2015, pp 311-343 from Springer

Abstract: Abstract This chapter is an introduction to reproducing kernel Kreĭn spaces and their interplay with operator valued Hermitian kernels. Existence and uniqueness properties are carefully reviewed. The approach used in this survey involves the more abstract, but very useful, concept of linearization or Kolmogorov decomposition, as well as the underlying concepts of Kreĭn space induced by a selfadjoint operator and that of Kreĭn space continuously embedded. The operator range feature of reproducing kernel spaces is emphasized. A careful presentation of Hermitian kernels on complex regions that point out a universality property of the Szegö kernels with respect to reproducing kernel Kreĭn spaces of holomorphic functions is included.

Keywords: Reproducing Kernel; Hermitian Kernel; Kolmogorov Decomposition; Selfadjoint Operator; Holomorphic Kernel (search for similar items in EconPapers)
Date: 2015
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-0348-0667-1_40

Ordering information: This item can be ordered from
http://www.springer.com/9783034806671

DOI: 10.1007/978-3-0348-0667-1_40

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().