Displaying similar documents to “Replicant compression coding in Besov spaces”

Some subclasses of close-to-convex functions

Adam Lecko (1993)

Annales Polonici Mathematici

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For α ∈ [0,1] and β ∈ (-π/2,π/2) we introduce the classes C β ( α ) defined as follows: a function f regular in U = z: |z| < 1 of the form f ( z ) = z + ∑ n = 1 ∞ a n z n , z ∈ U, belongs to the class C β ( α ) if R e e i β ( 1 - α ² z ² ) f ' ( z ) < 0 for z ∈ U. Estimates of the coefficients, distortion theorems and other properties of functions in C β ( α ) are examined.

Large dimensional sets not containing a given angle

Viktor Harangi (2011)

Open Mathematics

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We say that a set in a Euclidean space does not contain an angle α if the angle determined by any three points of the set is not equal to α. The goal of this paper is to construct compact sets of large Hausdorff dimension that do not contain a given angle α ∈ (0,π). We will construct such sets in ℝn of Hausdorff dimension c(α)n with a positive c(α) depending only on α provided that α is different from π/3, π/2 and 2π/3. This improves on an earlier construction (due to several authors)...

A general construction of nonseparable multivariate orthonormal wavelet bases

Abderrazek Karoui (2008)

Open Mathematics

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The construction of nonseparable and compactly supported orthonormal wavelet bases of L 2(R n); n ≥ 2, is still a challenging and an open research problem. In this paper, we provide a special method for the construction of such wavelet bases. The wavelets constructed by this method are dyadic wavelets. Also, we show that our proposed method can be adapted for an eventual construction of multidimensional orthogonal multiwavelet matrix masks, candidates for generating multidimensional...

Uniformly convex functions II

Wancang Ma, David Minda (1993)

Annales Polonici Mathematici

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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...