Spectral analysis of fourth order differential operators III

Abstract

This paper extends the results of the two previous papers in several directions. For one we allow slower decay of the coefficients, but higher order differentiability. For this an expansion for the diagonalizing transformations is derived. Secondly unbounded coefficients are permitted. This requires further transformations in order to achieve Levinson's form, but also a modification with the usual M-matrix approach. While the standard results carry over to weakly singular coefficients, very singular coefficients will generally lead to discrete spectra. (C) 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim