A Spectral Theory for Inner Functions

Spectral Theory and Special Functions

A short introduction to the use of the spectral theorem for self-adjoint operators in the theory of special functions is given. As the first example, the spectral theorem is applied to Jacobi operators, i.e. tridiagonal operators, on l(Z≥0), leading to a proof of Favard’s theorem stating that polynomials satisfying a three-term recurrence relation are orthogonal polynomials. We discuss the link...

A formula for the inner spectral radius

Exact observability, square functions and spectral theory

In the first part of this article we introduce the notion of a backwardforward conditioning (BFC) system that generalises the notion of zero-class admissibiliy introduced in [21]. We can show that unless the spectum contains a halfplane, the BFC property occurs only in siutations where the underlying semigroup extends to a group. In a second part we present a sufficient condition for exact obse...

Nuclear Matter Spectral Functions by Transport Theory

Quantum transport theory is used to calculate the nucleon spectral function in infinite nuclear matter. A self-consistent description is obtained by utilizing the relations between collision rates and correlation functions. Static and dynamical self-energies are taken into account in the single particle propagators. The real parts of the non-static selfenergy contributions are calculated by dis...

Approximate spectral functions in thermal field theory.

Causality requires that the ~anti!commutator of two interacting field operators vanishes for spacelike coordinate differences. This implies that the Fourier transform of the spectral function of this quantum field should vanish in the spacelike domain. We find that this requirement imposes some constraints on the use of resummed propagators in high temperature gauge theory. @S0556-2821~96!02418-6#