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On a modification of the Poisson integral operator

Dariusz Partyka (2011)

Annales UMCS, Mathematica

Given a quasisymmetric automorphism γ of the unit circle T we define and study a modification Pγ of the classical Poisson integral operator in the case of the unit disk D. The modification is done by means of the generalized Fourier coefficients of γ. For a Lebesgue's integrable complex-valued function f on T, Pγ[f] is a complex-valued harmonic function in D and it coincides with the classical Poisson integral of f provided γ is the identity mapping on T. Our considerations are motivated by the...

On a paper of Carleson.

Brakalova, Melkana A., Jenkins, James A. (2002)

Annales Academiae Scientiarum Fennicae. Mathematica

On a Problem of Best Uniform Approximation and a Polynomial Inequality of Visser

M. A. Qazi (2014)

Bulletin of the Polish Academy of Sciences. Mathematics

In this paper, a generalization of a result on the uniform best approximation of α cos nx + β sin nx by trigonometric polynomials of degree less than n is considered and its relationship with a well-known polynomial inequality of C. Visser is indicated.

On a radius problem concerning a class of close-to-convex functions

Richard Fournier (1995)

Banach Center Publications

The problem of estimating the radius of starlikeness of various classes of close-to-convex functions has attracted a certain number of mathematicians involved in geometric function theory ([7], volume 2, chapter 13). Lewandowski [11] has shown that normalized close-to-convex functions are starlike in the disc | z | < 4 2 - 5 . Krzyż [10] gave an example of a function f ( z ) = z + n = 2 a n z n , non-starlike in the unit disc , and belonging to the class H = f | f’() lies in the right half-plane. More generally let H* = f | f’() lies in...

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