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- W2561276543 abstract "The celebrated Hadamard's theorem on the multiplication of singularities (cf. e.g. [2], p. 82) has given rise to the investigation of the convolution (or Hadamard's product) h=f.g of two power s e r i e s f ( z ) = ~ a,z, g ( z ) = ~ b,,z, h(z) being defined as ~ anbn2 n. Let C be the class of normalized convex univalent functions. Some time ago G. P61ya and I. J. Schoenberg [6] conjectured that C is closed under convolution. In other words, iffeC and g ~C, then also f.g~C. This conjecture has been lately proved by St. Ruscheweyh and T. Sheil-Small [8]. T. J. Suffridge has also given an alternative proof of P61ya-Schoenberg conjecture, [9]. It is therefore quite a natural problem to look after another classes of functions closed under convolution. In this paper we shall be concerned with the class 2;k, 0 ~ 1} is a regular and univalent function with the Laurent series expansion" @default.
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- W2561276543 date "1976-01-01" @default.
- W2561276543 modified "2023-09-24" @default.
- W2561276543 title "Convolution and Quasieonformal Extension" @default.
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