Proves the sharp homogeneous entropy inequality for non-constant polynomials with zeros on the unit circle and determines the equality cases.
Israel Journal of Mathematics , volume =
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The paper establishes a linear lower bound on the number of atoms in extremal singular inner functions for the Krzyż conjecture and new equivalent conditions for its validity.
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Proof of the Agler--McCarthy entropy conjecture
Proves the sharp homogeneous entropy inequality for non-constant polynomials with zeros on the unit circle and determines the equality cases.
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Structural aspects of extremal functions in the Krzy\.z conjecture
The paper establishes a linear lower bound on the number of atoms in extremal singular inner functions for the Krzyż conjecture and new equivalent conditions for its validity.