A. Baranov, H. Woracek:

"Admissible majorants for de Branges spaces of entire functions";

in: "ASC Report 30/2007", issued by: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2007, ISBN: 978-3-902627-00-1.

For a given deBranges space H(E) we investigate deBranges sub-

spaces defined in terms of majorants on the real axis: if ! is a non-

negative function on R, we consider the subspace

R!(E) = ClosH(E)

F ∈ H(E) : ∃C > 0 : |E−1F| ≤ C! on R

.

We show that R!(E) is a deBranges subspace, describe all subspaces

of this form, and study the majorants ! such that R!(E) = H(E).

We give a criterion for the existence of positive minimal majorants

and characterize finite-dimensional subspaces of the form R!(E) in

terms of minimal majorants.

deBranges space, deBranges subspaces, majorants,

http://www.asc.tuwien.ac.at/preprint/2007/asc30x2007.pdf

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