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math.CV2026
A property of boundary extensions of atomic singular inner functions
Iason Efraimidis, Adrian Llinares, Sullivan MacDonald +2
Using a property of the Hilbert transform, we prove a measure theoretic result concerning the extensions of atomic singular inner functions to the circle. Various alternative proof…
math.CV2026
A convolution inequality and the Krzyż conjecture
Sullivan Francis MacDonald
Using a sharp bound for convolutions of non-negative trigonometric polynomials with the Fejér kernel resembling a pointwise variant of Bernstein's inequality for polynomials, we pr…
math.CV2026
Structural aspects of extremal functions in the Krzyż conjecture
Sullivan F. MacDonald
Extremal functions for the th coefficient in the Krzyż conjecture are atomic singular inner functions with at most atoms. This paper gives a lower bound on the number of ato…