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Semihyperbolic entire functions
Nonlinearity, 2002The concept of ``semihyperbolicity'' is applied to transcendental entire functions and related to the dynamics and the geometry of the Julia set. A transcendental function \(f\) is called ``semihyperbolic'' at some \(a\in{\mathbb C}\) if \(a\) has a neighborhood \(V\) and an \(N\in{\mathbb N}\) such that for every \(n\in {\mathbb N}\) and every ...
Bergweiler, Walter, Morosawa, Shunsuke
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Entire Mean Periodic Functions
Canadian Journal of Mathematics, 1975Let H denote the set of all entire functions of a single complex variable equipped with the topology of convergence uniform on all compact subsets of C, the set of complex numbers. Then an entire function f is mean periodic if the subspace spanned by f and its complex translates is not dense in H. It was shown by Schwartz [13, p.
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Nevanlinna Matrices of Entire Functions
Mathematische Nachrichten, 1995AbstractThe notion of a pre‐Nevanlinna matrix of entire functions is introduced, and we find necessary and sufficient conditions for an entire function to belong to such a matrix, thereby generalizing previous work of Krein.If one of the functions in a pre‐Nevanlinna matrix is a polynomial, then the three others arc also polynomials and their degrees ...
Berg, Christian, Pedersen, Henrik L.
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Mathematical Proceedings of the Cambridge Philosophical Society, 1993
AbstractIt has been observed that lacunary functions and random functions often have many properties in common (cf. [5]). The present paper has the object of showing that lacunary entire functions behave in many respects like random entire functions. Both have the property of being large except in very small neighbourhoods of their zeros and these have
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AbstractIt has been observed that lacunary functions and random functions often have many properties in common (cf. [5]). The present paper has the object of showing that lacunary entire functions behave in many respects like random entire functions. Both have the property of being large except in very small neighbourhoods of their zeros and these have
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2012
Consider the space of nonconstant entire functions \(\mathcal{E}\) with the topology of uniform convergence on compact subsets of \(\mathbb{C}\) and with the action of \(\mathbb{C}\) by translation. A minimal entire function is a nonconstant entire function f with the property that for any \(g \in \mathcal{E}\) which is a limit of translates of f, in ...
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Consider the space of nonconstant entire functions \(\mathcal{E}\) with the topology of uniform convergence on compact subsets of \(\mathbb{C}\) and with the action of \(\mathbb{C}\) by translation. A minimal entire function is a nonconstant entire function f with the property that for any \(g \in \mathcal{E}\) which is a limit of translates of f, in ...
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The expanding regulatory mechanisms and cellular functions of circular RNAs
Nature Reviews Molecular Cell Biology, 2020Ling-Ling Chen
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Gene regulation by long non-coding RNAs and its biological functions
Nature Reviews Molecular Cell Biology, 2020Luisa Statello +2 more
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