With each resonance of the Laplacian acting on compactly supported sections a homogeneous vector bundle over Riemannian symmetric space non-compact type, One can associate residue representation. The purpose this paper is to study them. assumed have rank-one but irreducible representation {\tau} K defining arbitrary. We give an algorithm that aims at determining if these representations are irr...

By studying the integrated density of states, we prove the existence of Lyapunov exponents and the Thouless formula for the Schrödinger operator −d2/dx2 + cos xν with 0 < ν < 1 on L2[0,∞). This yields an explicit formula for these Lyapunov exponents. By applying rank one perturbation theory, we also obtain some spectral consequences.

The closed-loop form of a second-order hyperbolic system with scalar collocated sensor/actuator is considered. The Riesz basis property of the system is verified for diagonal semigroups based on an abstract result of one rank perturbation of discrete-type operators in Hilbert spaces. A simplified proof for the abstract result is presented.

Abstract It is shown that the relative distance in Frobenius norm of a real symmetric order- d tensor rank-two to its best rank-one approximation upper bounded by $$\sqrt{1-(1-1/d)^{d-1}}$$ 1 - ( / d ) <...