Discreteness of the spectrum of second-order differential operators and associated embedding theorems

[摘要] Necessary and sufficient conditions and also simple sufficient conditions are given for the self-adjoint operators associated with the second-order linear differential expression [GRAPHICS] on [a,b) to have discrete spectrum. Here the coefficients Of tau are non-negative and satisfy minimal smoothness conditions. These results follow from compact embedding theorems from a weighted one-dimensional Sobolev space with norm (integral(a)(b)(p\f(1)\(r) + q\f\(r)))(l/r) into a weighted Banach space with norm (integral(a)(b)w\f\(s))(l/s). (C) Elsevier Science (USA).

[发布日期] 2002-09-20

[关键词] Sturm-Liouville operator;discrete spectrum;compact embedding