# Spectral bounds for indefinite singular Sturm-Liouville operators with uniformly locally integrable potentials

The non-real spectrum of a singular indefinite Sturm-Liouville operator A=1/r (-d/dx p d/dx+q) with a sign changing weight function r consists (under suitable additional assumptions on the real coefficients 1/p,q,r in L^1_loc(R)) of isolated eigenvalues with finite algebraic multiplicity which are symmetric with respect to the real line. In this paper bounds on the absolute values and the imaginary parts of the non-real eigenvalues of A are proved for uniformly locally integrable potentials q and potentials \$q in L^s(R) for some s in [1,\infty]. The bounds depend on the negative part of q, on the norm of 1/p and in an implicit way on the sign changes and zeros of the weight function.

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Behrndt, Jussi / Schmitz, Philipp / Trunk, Carsten: Spectral bounds for indefinite singular Sturm-Liouville operators with uniformly locally integrable potentials. Ilmenau 2019.

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