Abstract
which is satisfied by x yj(t) at t = 0). According to Weyl [3], p. 238, the assumption (2) precludes the existence of a A0 corresponding to which (3) had two linearly independent solutions of class (L2). Correspondingly, every boundary condition (5) determines for (1) a spectrum S(p), containing a (possibly vacuous) point spectrum P(p). The latter consists of those values A0 corresponding to which there exists an x y(t) satisfying (3), (4), (5). A theorem of Weyl implies that the cluster values of S(p), that is, of the set consisting of the continuous spectrum and the derivative of the point spectrum, is independent of 0; cf. [3], pp. 251-252. This invariant A-set, S'(q), can therefore be denoted
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