The Krzyż conjecture revisited

DOI10.1016/j.aim.2014.12.031zbMath1310.30045arXiv1311.7668OpenAlexW1535191787WikidataQ123198663 ScholiaQ123198663MaRDI QIDQ2253808

María J. Martín, Ignacio Uriarte-Tuero, Dragan Vukotić, Eric T. Sawyer

Publication date: 13 February 2015

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1311.7668

zbMATH Keywords

variational methodsTaylor coefficientsbounded analytic functionsnon-linear extremal problem

Mathematics Subject Classification ID

Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.) (30C45) Spaces of bounded analytic functions of one complex variable (30H05) Coefficient problems for univalent and multivalent functions of one complex variable (30C50)

Related Items (9)

Idempotent Fourier multipliers acting contractively on \(H^p\) spaces ⋮ Classes of analytic functions related to Blaschke products ⋮ F. Wiener's trick and an extremal problem for \(H^p\) ⋮ Sums of squares. I: Scalar functions ⋮ Sums of squares. II: Matrix functions ⋮ Subclasses of starlike functions related to Blaschke products ⋮ On univalent polynomials with critical points on the unit circle ⋮ Analogues to Landau's inequality for nonvanishing bounded functions and for Bloch functions ⋮ The Krzyż conjecture and an entropy conjecture

Cites Work

• A proof of the Bieberbach conjecture
• Coefficients of nonvanishing functions in \(H^\infty\)
• A coefficient problem for bounded nonvanishing functions
• Coefficients of bounded nonvanishing functions
• A variational method for functions with positive real part
• A Variational Method for Starlike Functions
• On a coefficient problem for nonvanishing H ^p functions
• Foundations of the theory of extremal problems for bounded analytic functions and various generalizations of them
• Iteration of functions subordinate to schlicht functions
• The Curious History of Faa di Bruno's Formula
• A Proof of Krzyż's Conjecture for the Fifth Coefficient
• Bounded nonvanishing functions and bateman functions
• Local extremal problems for bounded analytic functions without zeros
• Schwarz-Pick Type Inequalities
• The Coefficients of Multivalent Close-to-Convex Functions
• Some properties of extremal functions for Krzyz problem
• Applications of subordination theory to the class of bounded nonvanishing functions
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