## Linear and Complex Analysis Problem Book 3, Part 2Victor P. Havin, Nikolai K. Nikolski The 2-volume-book is an updated, reorganized and considerably enlarged version of the previous edition of the Research Problem Book in Analysis (LNM 1043), a collection familiar to many analysts, that has sparked off much research. This new edition, created in a joint effort by a large team of analysts, is, like its predecessor, a collection of unsolved problems of modern analysis designed as informally written mini-articles, each containing not only a statement of a problem but also historical and metho- dological comments, motivation, conjectures and discussion of possible connections, of plausible approaches as well as a list of references. There are now 342 of these mini- articles, almost twice as many as in the previous edition, despite the fact that a good deal of them have been solved! |

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### Contents

Banach spaces ed by S Kisliakov | 1 |

Banach algebras ed by H Dales and A Helemskii | 51 |

27 F Forelli Divisibility problem in AD and HB | 70 |

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Akad algebra Amer Anal analytic capacity analytic functions answer asymptotic Banach Banach space Bergman space boundary bounded Carleson characterization closed coefficients compact set complex condition conformal mapping conjecture connected constant continuous convergence curve defined denote Department of Mathematics differential disc Dokl domain dynamics English transl entire functions equations example exists exponential type finite Fourier funkt geometric harmonic measure Hausdorff Hausdorff measure holomorphic functions holomorphic mappings Hruscev implies inequality Inst integral interpolation Julia set Kharkov Lebesgue Lebesgue measure Lemma linear Nauk SSSR norm operator orthogonal polynomials polynomially convex positive preprint problem Proc proof proved quadratic question rational approximation rational functions rational maps References result Riemann Russian satisfying sequence singularities solution Soviet Math space Steklov subharmonic functions subspace Suppose theorem theory topology unique unit disk Univ univalent functions v.old variables zero