Nathan Walsh

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20202022

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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…