Thomas Ransford

activity

20232026

collaborators

5 papers

math.CA2026

A functional inequality related to Domar's uniform boundedness theorem

Thomas Ransford

We study the functional inequality \[ f(r+s)\le g(r)+αf(s) \quad(r,s>0). \] Here $g : (0, \infty) \to [0, \infty)$ is a given decreasing function, $α$ is a constant such that $0 < α < 1$ , an…

math.FA2026

A proof of Esterle's conjecture on negative powers of Hilbert-space contractions

Thomas Ransford

We establish the following result, confirming a conjecture of Jean Esterle. For each closed subset $E$ of the unit circle of Lebesgue measure zero, there exists a positive sequence…

math.FA2024

Contractivity of Möbius functions of operators

Thomas Ransford, Dashdondog Tsedenbayar

Let $T$ be a injective bounded linear operator on a complex Hilbert space. We characterize the complex numbers $λ, μ$ for which $(I + λ T) (I + μ T)^{- 1}$ is a contraction, the characteriz…

math.FA2024

On the real and imaginary parts of powers of the Volterra operator

Thomas Ransford, Dashdondog Tsedenbayar

We study the real and imaginary parts of the powers of the Volterra operator on $L^{2} [0, 1]$ , specifically their eigenvalues, their norms and their numerical ranges.

math.FA2023

Negative powers of Hilbert-space contractions

Thomas Ransford

We show that, given a closed subset $E$ of the unit circle of Lebesgue measure zero, there exists a positive sequence $u_{n} \to \infty$ with the following property: if $T$ is a Hilber…