2008•Journal of Physics A Mathematical and TheoreticalRequires access

Accumulation of complex eigenvalues of indefinite Sturm–Liouville operators

Jussi Behrndt, Qutaibeh Katatbeh, Carsten Trunk

Abstract

Spectral properties of singular Sturm-Liouville operators of the form A = sgn ()(− d2 dx2 + V ) with the indefinite weight x 7→ sgn (x) on R are studied. For a class of potentials with lim|x|!1 V (x) = 0 the accumulation of complex and real eigenvalues of A to zero is investigated and explicit eigenvalue problems are solved numerically.

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Key concepts: Sturm–Liouville theory, Eigenvalues and eigenvectors, Mathematics, Class (philosophy), Spectrum (functional analysis), Pure mathematics, Zero (linguistics), Mathematical analysis