Title: Eigenfunction expansion and subordinacy theory of Jacobi operators on Z
 
Abstract: If T is a self-adjoint operator on a finite-dimensional Hilbert space H, then any vector v in H can be
written as a linear combination of eigenfunctions of T. The concept of eigenfunction expansion is the
generalization of this fact to infinite-dimensional Hilbert spaces. In this talk, we introduce this concept
in the specific case of Jacobi operators on ℓ2(Z). In particular, we will present the connection between
eigenfunction expansion and subordinacy theory, which relates asymptotic properties of solutions to
the eigenvalue equation to singularity properties of spectral measures.