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Reproducing Kernel Krein Spaces Of Analytic Functions And Inverse Scattering, Daniel Alpay
Reproducing Kernel Krein Spaces Of Analytic Functions And Inverse Scattering, Daniel Alpay
Mathematics, Physics, and Computer Science Faculty Articles and Research
The purpose of this thesis is to study certain reproducing kernel Krein spaces of analytic functions, the relationships between these spaces and an inverse scattering problem associated with matrix valued functions of bounded type, and an operator model.
Roughly speaking, these results correspond to a generalization of earlier investigations on the applications of de Branges' theory of reproducing kernel Hilbert spaces of analytic functions to the inverse scattering problem for a matrix valued function of the Schur class.
The present work considers first a generalization of a portion of de Branges' theory to Krein spaces. We then formulate a general …