Title

On a New Class of Structured Reproducing Kernel Spaces, Journal of Functional Analysis

Document Type

Article

Publication Date

1993

Abstract

A class of reproducing kernel spaces with reproducing kernels of the form Kω(λ) = {J − Θ(λ)JΘ(ω)*}/ρω(λ) with pω(λ) = a(λ)a(ω)* is characterized in terms of invariance under a pair of generalized shift operators and a structural identity. This incorporates a characterization of de Branges for the "line" case and a later analogue due to Ball for the "circle" case, as well as many other possibilities, by specializing the choice of ρ. These results also permit the extension of some earlier characterizations by the authors of finite dimensional spaces with reproducing kernels of the form given above to the infinite dimensional case. The non-Hermitian case is also considered.

Comments

This article was originally published in Journal of Functional Analysis, volume 111, in 1993. DOI: 10.1006/jfan.1993.1001

Peer Reviewed

1

Copyright

Elsevier