Nathan Walsh

activity

20202022

collaborators

3 papers

math.FA2022

Norms of polynomials of the Volterra operator

Thomas Ransford, Nathan Walsh

We compute the operator norm of real-quadratic polynomials of the Volterra operator. This is used to test whether the Crouzeix conjecture holds for the Volterra operator.

math.FA2021

A four-mean theorem and its application to pseudospectra

Thomas Ransford, Nathan Walsh

Let $N \geq 4$ . We show that, if $x_{1}, \dots, x_{N}$ and $y_{1}, \dots, y_{N}$ are $N$ -tuples of strictly positive numbers whose arithmetic, geometric and harmonic means agree, then \[ \max_j…

math.SP2020

Spectral sets, extremal functions and exceptional matrices

Thomas Ransford, Nathan Walsh

Let $A$ be a square matrix and let $Ω$ be an open set in the plane containing the spectrum of $A$ . We consider the problem of maximizing the operator norm $∥ f (A) ∥$ amongst all ho…