Universal entire functions with gap power series

Luh, Wolfgang; Martirosian, Valeri A.; Müller, Jürgen

doi:10.1016/s0019-3577(98)80032-3

Cited by 16 publications

(23 citation statements)

References 7 publications

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“…The author [Gro87] showed that the set of monsters is residual in H(O) and also obtained some kinds of monsters in arbitrary open sets. Monsters with additional universality and other properties were constructed by Luh [Luh97] and Schneider [Scn97]; see also [LMM99 + ]. Kanatnikov [Kan80], [Kan84] studies universal boundary behaviour (only of f itself) for meromorphic functions.…”

Section: Theorem 16 (Luh) Let O ⊂ C O = C Be An Open Set With Simpmentioning

confidence: 99%

Universal families and hypercyclic operators

Grosse‐Erdmann

1999

Bull. Amer. Math. Soc.

514

389

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Section: Theorem 16 (Luh) Let O ⊂ C O = C Be An Open Set With Simpmentioning

confidence: 99%

Universal families and hypercyclic operators

Grosse‐Erdmann

1999

Bull. Amer. Math. Soc.

514

389

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“…Monster with additional properties were also constructed by Luh [32], Schneider [39] (monsters with properties of univalence) and Luh, Martirosian and Müller [33] (monsters with gap power series). Kanatnikov [26,27] studied in the eighties universal boundary behavior (only of f itself) for meromorphic functions.…”

Section: (2) For Every Bounded Measurable Set S ⊂ C T (F G T S) =mentioning

confidence: 99%

Maximal cluster sets on spaces of holomorphic functions

Prado-Bassas¹,

Antonio²

2008

Analysis

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“…The first one is classic and can be found in [13, Theorem 9.1.4]. The second one is a recent lacunary result and may be seen in [26,Lemma] and [28,Lemma], see also [27,Lemma 2]. A little further terminology is in order.…”

Section: Consider the Operator E : § -> S Given By Ef(z) = Zf'iz)mentioning

confidence: 99%

“…By Mergelyan's theorem, there exists a polynomial P t such that (14) \g ( where / : £2 -> C is defined as [26] (16)…”

Section: Consider the Operator E : § -> S Given By Ef(z) = Zf'iz)mentioning

confidence: 99%

U-Operators

Bernal–González¹,

Prado-Tendero²

2005

J. Aust. Math. Soc.

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Inspired by a statement of W. Luh asserting the existence of entire functions having together with all their derivatives and antiderivatives some kind of additive universality or multiplicative universality on certain compact subsets of the complex plane or of, respectively, the punctured complex plane, we introduce in this paper the new concept of U-operators, which are defined on the space of entire functions. Concrete examples, including differential and antidifferential operators, composition, multiplication and shift operators, are studied. A result due to Luh, Martirosian and Miiller about the existence of universal entire functions with gap power series is also strengthened.2000 Mathematics subject classification: primary 30E10; secondary 47A16, 47B33, 47B38, 47E05, 47G10.

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Universal entire functions with gap power series

Cited by 16 publications

References 7 publications

Universal families and hypercyclic operators

Universal families and hypercyclic operators

Maximal cluster sets on spaces of holomorphic functions

U-Operators

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