On the Spectrum of a Class of Differential Operators and Embedding Theorems

The author considers the embedding problem of weighted Sobolev spaces H. . in weighted L. spaces L. . , and some sufficient conditions and necessary conditions are given, when weight functions satisfy certain conditions. The author uses the results obtained to the qualitative analysis of the spectrum of 2n-order weighted differential operator, and gives some sufficient conditions and necessary conditions to ensure that the spectrum is discrete.