Jonathan Eckhardt, Gerald Teschl
Sturm-Liouville Operators with Measure-Valued Coefficients
Preprint series: ESI preprints

MSC:

34B20 Weyl theory and its generalizations

34L05 General spectral theory

34B24 Sturm-Liouville theory, See also {34Lxx}

47A10 Spectrum, resolvent

Abstract: We give a comprehensive treatment of Sturm--Liouville operators with measure-valued coefficients
including, a full discussion of self-adjoint extensions and boundary conditions, resolvents,
and Weyl--Titchmarsh theory. We avoid previous technical restrictions and, at the same time,
extend all results to a larger class of operators. Our operators include classical
Sturm--Liouville operators, Lax operators arising in the treatment of the Camassa--Holm
equation, Jacobi operators, and Sturm--Liouville operators on time scales as special cases.


Keywords: Schrodinger operators, spectral theory, strongly singular potentials