Some Generalizations and Supplements
摘要
In this Chapter, we generalize some results of the previous chapters and give some complementary comments. We discuss in detail the scope of the methods of Chaps. 2 , 3 and 6 . The first section of this chapter is the introduction. In the second, third and fourth sections, we generalize the asymptotic formulasAsymptotic formulas for the eigenvalues and eigenfunctions obtained in Sects. 2.3 and 6.2 for different boundary value problems for the scalar Schrödinger operators, vector Schrödinger operators and differential operators of higher order, respectively. In the fifth section we consider the spectral expansion for the higher order differential operatorsDifferential operator and study the asymptotically spectral differential operatorsDifferential operator of higher order. In the last section of this chapter, we consider the spectra of the differential operators of higher order with periodic PT-symmetric coefficients.