A Strong Szegő Theorem for Jacobi Matrices

A Strong Szegő Theorem for Jacobi Matrices

“…We will use the notation x y if x ≤ cy for some constant c > 0 (which may change from one line to the next). We will also need the following lemma, which is a special case of Lemma 2.4 in [1]:…”

“…In this erratum an error in [1] is pointed out and corrected. In that paper we were concerned with the spectral theory of Jacobi matrices, that is semi-infinite tridiagonal matrices where a n > 0 and b n ∈ R. We assume that a 2 n − 1 and b n are conditionally summable and define for n = 0, 1, .…”

“…The goal of Sect. 5 of [1] was to prove the following result (which appears there as Proposition 5.1):…”

“…In [1] we attempted to use Asymptotic Integration to prove this proposition. Due to two separate multiplication errors Eqs.…”

“…So far our attempts to resurrect the Asymptotic Integration argument have failed, so instead in the next section we present a complete proof of Proposition 1.1 based on a contraction mapping argument. With these corrections the remainder of the argument in [1] is valid as stated.…”