Normal Differential Operators of Third Order

Authors : Zi ISMAİLOV, M EROL

Pages : 675-688

View : 25 | Download : 14

Publication Date : 2012-05-01

Article Type : Research Paper

Abstract :In the Hilbert space of vector-functions L 2 insert ignore into journalissuearticles values(Hinsert ignore into journalissuearticles values(a, b););, where H is any separable Hilbert space, the general representation in terms of boundary values of all normal extensions of the formally normal minimal operator, generated by linear differential-operator expressions of third order in the form linsert ignore into journalissuearticles values(u); = u ′′′insert ignore into journalissuearticles values(t); + A 3 uinsert ignore into journalissuearticles values(t);, A : Dinsert ignore into journalissuearticles values(A); ⊂ H → H, A = A ∗ ≥ E, is obtained in the first part of this study. Then, some spectral properties of these normal extensions are investigated. In particular, the case of A −1 ∈ S∞insert ignore into journalissuearticles values(H);, asymptotic estimates of normal extensions of eigenvalues has been established at infinity.
Keywords : Normal extension, Compact operator, Eigenvalue, Asymptotical behavior of eigenvalues, 2000 AMS Classification 47 A 20