2021
DOI: 10.48550/arxiv.2112.09558
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Canonical systems and quantum graphs

Abstract: The representation of the resolvent as an integral operator, the m function, and the associated spectral representation are fundamental topics in the spectral theory of self-adjoint ordinary differential operators. Versions of these are developed here for canonical systems Ju ′ = −zHu of arbitrary order. A classical result shows that canonical systems of order two can be used to realize arbitrary spectral data, in the form of m functions from the upper half plane to itself. In this paper, canonical systems on … Show more

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