Acta Sci. Math. (Szeged)

. The spectral theory of the equation changes depending on the growth of H towards the endpoint s+; the classical distinction into the Weyl alternatives ‘limit point’ or ‘limit circle’ case. A refined measure for the growth of a limit point Hamiltonian H can be obtained by comparing with Hpolynomials. This growth measure is concretised by a number∆(H) ∈ N0∪{∞} and appeared first in connection with a Pontryagin space analogue of the equation (∗). It is known that the growth restriction ‘∆(H) < ∞’ has some striking consequences on the spectral theory of the equation; in many respects, the case ‘limit point but still ∆(H) < ∞’ is similar to the limit circle case. In general, the number ∆(H) is given in a rather implicit way, difficult to handle and not suitable for concrete calculations. In the present paper we provide a more accessible way to compute ∆(H) for some particular classes of Hamiltonians which occur in connection with Sturm–Liouville equations and Krĕın strings.