We will consider in this talk non-self-adjoint operators in Hilbert
spaces given as relatively compact perturbations of a self-adjoint
operator. Typical examples are Schrödinger operators with bounded,
complex potentials vanishing at infinity. We will describe abstract
conditions ensuring that the Hilbert space admits a direct sum
decomposition into H-invariant subspaces, generalizing the well-known
spectral decomposition of self-adjoint operators in terms of their
spectral measures. A central role in the talk will be played by spectral
singularities, an abstract notion corresponding to that of real
resonances for Schrödinger operators. We will also present a useful
regularized functional calculus for non-self-adjoint operators.
This is joint work with Nicolas Frantz.
Meeting ID: 814 591 7621
Passcode: 147983