Reproducing Kernel Kreı̆n Spaces

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

Chapter 22 in Operator Theory, 2026, pp 551-583 from Springer

Abstract: Abstract This chapter is an introduction to reproducing kernel Kreı̆n 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 Kreı̆n space induced by a selfadjoint operator and that of Kreı̆n 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 Kreı̆n spaces of holomorphic functions is included.

Date: 2026
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DOI: 10.1007/978-3-032-16356-1_40

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