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.
Recommended Citation
D. Alpay and H. Dym. On a new class of structured reproducing kernel spaces, Journal of functional analysis, vol. 111 (1993), 1-28.
Peer Reviewed
1
Copyright
Elsevier
Comments
This article was originally published in Journal of Functional Analysis, volume 111, in 1993. DOI: 10.1006/jfan.1993.1001