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Coefficients of functions with bounded boundary rotation

1971
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Proceedings of the American Mathematical Society
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For k ê2 denote by Vk the class of normalized functions analytic in the unit disc which have boundary rotation at most kir. For fixed «e(¿+6)/4 we determine the maximum of the set of values of \a"\, where an is the nth Taylor coefficient of a function in Vk. For a fixed k 2:2 let Vk denote the class of functions (1) f(z) = 3 + a2z2 + a3z3 Hwhich are analytic in U= {z:\z\ <1{ and have an integral representation of the form (2) f'(z) = exp j-j log(l -ze-^-'d^tyl , where p(t) is real-valued and of

doi:10.1090/s0002-9939-1971-0274738-5
fatcat:dtjd4ebc7rhxvkhowj4xaw23d4