THE BASIS PROPERTY OF STURM-LIOUVILLE PROBLEMS WITH BOUNDARY CONDITIONS DEPENDING QUADRATICALLY ON THE EIGENPARAMETER

We study basisness of root functions of Sturm-Liouville problems with a boundary conditiondepending quadratically on the spectral parameter. We determine the explicit form of thebiorthogonal system. Using this we prove that the system of root functions, with arbitrarytwo functions removed, form a minimal system in L2, except some cases where this system isneither complete nor minimal. For the basisness in L2 we prove that the part of the root spaceis quadratically close to systems of sines and cosines. We also consider these basis propertiesin the context of general Lp. 2000 Mathematics Subject Classification. 34L10, 34B24, 34L20.