Weakly stationary processes with non–positive autocorrelations

Šárka Došlá; Jiří Anděl

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Solving some problems of advanced analytical nature posed in the SIAM Review. II.

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Distributions of sojourn time, maximum and minimum for pseudo-processes governed by higher-order heat-type equations.

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Uniformly convex functions II

Wancang Ma, David Minda (1993)

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Recently, A. W. Goodman introduced the class UCV of normalized uniformly convex functions. We present some sharp coefficient bounds for functions f(z) = z + a₂z² + a₃z³ + ... ∈ UCV and their inverses $f^{- 1} (w) = w + d ₂ w ² + d ₃ w ³ + . . .$ . The series expansion for $f^{- 1} (w)$ converges when $| w | < ϱ_{f}$ , where $0 < ϱ_{f}$ depends on f. The sharp bounds on $| a_{n} |$ and all extremal functions were known for n = 2 and 3; the extremal functions consist of a certain function k ∈ UCV and its rotations. We obtain the sharp bounds on $| a_{n} |$ and all extremal functions for...