Abstract:Part I of this paper deals with two-dimensional canonical systems y ′ (x) = yJH(x)y(x), x ∈ (a, b), whose Hamiltonian H is non-negative and locally integrable, and where Weyl's limit point case takes place at both endpoints a and b. We investigate a class of such systems defined by growth restrictions on H towards a. For example, Hamiltonians on (0, ∞) of the form H(x) := x −α 0 0 1where α < 2 are included in this class. We develop a direct and inverse spectral theory parallel to the theory of Weyl and de Bran… Show more
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