Self-adjoint analytic operator functions and their local spectral function

Spectral Behaviour of a Simple Non-self-adjoint Operator

We investigate the spectrum of a typical non-selfadjoint differential operator AD = −d2/dx2 ⊗ A acting on L(0, 1) ⊗ C, where A is a 2 × 2 constant matrix. We impose Dirichlet and Neumann boundary conditions in the first and second coordinate respectively at both ends of [0, 1] ⊂ R. For A ∈ R we explore in detail the connection between the entries of A and the spectrum of AD, we find necessary c...

Spectral properties of unbounded JJ-self-adjoint block operator matrices

We study the spectrum of unbounded J-self-adjoint block operator matrices. In particular, we prove enclosures for the spectrum, provide a sufficient condition for the spectrum being real and derive variational principles for certain real eigenvalues even in the presence of non-real spectrum. The latter lead to lower and upper bounds and asymptotic estimates for eigenvalues. AMS Subject classifi...

Triple variational principles for self-adjoint operator functions

Article history: Received 13 June 2013 Accepted 3 September 2015 Available online 19 January 2016 Communicated by L. Gross MSC: primary 49R05 secondary 47A56, 47A10

Weyl Function and Spectral Properties of Self-adjoint Extensions

The Laplace operator is essentially self-adjoint