Point mass insertion on the real line and non-exponential perturbation of the recursion coefficients

TL;DR

This paper constructs a probability measure on the real line where adding a point mass causes non-exponential changes in the recursion coefficients, challenging typical decay assumptions.

Contribution

It introduces a measure with a point mass that induces non-exponential perturbations in recursion coefficients, providing new insights into spectral theory.

Findings

Adding a point mass causes non-exponential changes in recursion coefficients.

The constructed measure has compact support on the real line.

This work challenges assumptions about exponential decay in spectral perturbations.

Abstract

We present the construction of a probability measure with compact support on R such that adding a discrete pure point results in changes in the recursion coefficients without exponential decay.