collaborators

6 papers

math.FA2026

Sharp spectral constants for scaled -numerical ranges

Mohamed Amine Aouichaoui, Ryan O'Loughlin

For , and , let be the scaled -numerical range. We prove that for every , \[ Ω_{η(γ)}(A) =\bigcup_{κ…

math.CV2026

A Schwarz-Jack lemma, circularly symmetric domains and numerical ranges

Javad Mashreghi, Annika Moucha, Ryan O'Loughlin +2

We prove a Schwarz-Jack lemma for holomorphic functions on the unit disk with the property that their maximum modulus on each circle about the origin is attained at a point on the…

math.FA2026

-Numerical Ranges and Spectral Sets

Ryan O'Loughlin, Jyoti Rani

We study spectral constants for convex domains containing the spectrum of an operator. We extend the Crouzeix--Palencia framework by obtaining bounds depending on a parameter…

math.FA2025

Describing the Numerical Range and -Numerical Range of Matrices via Their Unitary Orbits and the Joukowsky Transform

Ryan O'Loughlin

We generalise the Elliptical Range Theorem to characterise the numerical range of matrices belonging to a subspace of the space of \(3 \times 3\) matrices. Using Specht's Theorem,…

math.FA2025

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

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

Given a compact convex planar domain with non-empty interior, the classical Neumann's configuration constant is the norm of the Neumann-Poincaré operator…

math.FA2025

Bounded Toeplitz Products on the Hardy Space

Ryan O'Loughlin

A Toeplitz operator on the Hardy space of the unit circle is bounded if and only if its symbol is bounded. For two Toeplitz operators, there are no known function-theoretic conditi…