Chains of reproducing kernel Hilbert spaces generated by unimodular functions
[Chaînes d’espaces de Hilbert à noyau reproduisant générés par des fonctions unimodulaires]
Suzuki, Masatoshi1
1 Department of Mathematics, School of Science, Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro-ku, Tokyo 152-8551, Japan
Annales de l'Institut Fourier, Online first, 46 p.

Nous présentons une méthode pour construire une chaîne d’espaces de Hilbert à noyau reproduisant contrôlés par un système d’équations différentielles du premier ordre à partir d’une fonction unimodulaire donnée satisfaisant plusieurs conditions. L’une des applications de cette méthode est une solution conditionnelle mais richement générale au problème inverse de la récupération de l’hamiltonien de structure à partir d’un espace de Branges donné.

We present a method to construct a chain of reproducing kernel Hilbert spaces controlled by a first-order system of differential equations from a given unimodular function satisfying several conditions. One of the applications of that method is a conditional but richly general solution to the inverse problem of recovering the structure Hamiltonian from a given de Branges space.

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DOI : 10.5802/aif.3705
Classification : 34A55, 31A10, 34L40, 47B35
Keywords: de Branges spaces, inverse problem, structure Hamiltonians, reproducing kernel Hilbert spaces, unimodular functions
Mots-clés : espaces de Branges, problème inverse, Hamiltoniens de structure, espaces de Hilbert à noyau reproduisant, fonctions unimodulaires

Suzuki, Masatoshi 1

1 Department of Mathematics, School of Science, Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro-ku, Tokyo 152-8551, Japan 
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Suzuki, Masatoshi. Chains of reproducing kernel Hilbert spaces generated by unimodular functions. Annales de l'Institut Fourier, Online first, 46 p.

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