THE SPECTRAL THEORY OF 2ND-ORDER 2-POINT DIFFERENTIAL-OPERATORS .2. ASYMPTOTIC EXPANSIONS AND THE CHARACTERISTIC DETERMINANT

[摘要] In this second paper of a four-part series, we construct the characteristic determinant of a two-point differential operator L in L(2)[0, 1], where L is determined by l = -D-2+q and by independent boundary values B-1, B-2. For the solutions u(.;rho) and upsilon(.;rho) of the differential equation rho(2)u+u''-qu=0 with u(1;rho)=e(i rho), u'(1;rho)=i rho e(i rho) and upsilon(0;rho)=1, upsilon'(0;rho)=-i rho, asymptotic formulas are established on a half plane Im rho greater than or equal to-d. Then u(.;rho) and upsilon(.;rho) lead to the characteristic determinant Delta(rho) of L, which also satisfies an asymptotic formula on Im rho greater than or equal to-d. (C) 1994 Academic Press, Inc.

[发布日期] 1994-11-01