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Distance formulae and invariant subspaces, with an application to localization of zeros of the Riemann ζ -function

Nikolai Nikolski (1995)

Annales de l'institut Fourier

It is proved that a subspace of a holomorphic Hilbert space is completely determined by their distances to the reproducing kernels. A simple rule is established to localize common zeros of a subspace of the Hardy space of the unit disc. As an illustration we show a series of discs of the complex plan free of zeros of the Riemann ζ -function.

Distortion function and quasisymmetric mappings

J. Zając (1991)

Annales Polonici Mathematici

We study the relationship between the distortion function Φ K and normalized quasisymmetric mappings. This is part of a new method for solving the boundary values problem for an arbitrary K-quasiconformal automorphism of a generalized disc on the extended complex plane.

Distribution of zeros and shared values of difference operators

Jilong Zhang, Zongsheng Gao, Sheng Li (2011)

Annales Polonici Mathematici

We investigate the distribution of zeros and shared values of the difference operator on meromorphic functions. In particular, we show that if f is a transcendental meromorphic function of finite order with a small number of poles, c is a non-zero complex constant such that Δ c k f 0 for n ≥ 2, and a is a small function with respect to f, then f Δ c k f equals a (≠ 0,∞) at infinitely many points. Uniqueness of difference polynomials with the same 1-points or fixed points is also proved.

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