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math.CV2025
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.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
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…