Ryan O’Loughlin

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20242026

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math.FA2024

On the Crouzeix ratio for $N \times N$ matrices

Bartosz Malman, Javad Mashreghi, Ryan O'Loughlin +1

The Crouzeix ratio $ψ (A)$ of an $N \times N$ complex matrix $A$ is the supremum of $∥ p (A) ∥$ taken over all polynomials $p$ such that $∣ p ∣ \leq 1$ on the numerical range of $A$ . It i…

math.FA2024

Double-layer potentials, configuration constants and applications to numerical ranges

Bartosz Malman, Javad Mashreghi, Ryan O'Loughlin +1

Given a compact convex planar domain $Ω$ with non-empty interior, the classical Neumann's configuration constant $c_{R} (Ω)$ is the norm of the Neumann-Poincaré operator $K…

On the Crouzeix ratio for N×N matrices

Double-layer potentials, configuration constants and applications to numerical ranges

On the Crouzeix ratio for $N \times N$ matrices