The Hier metric space, the existence theorem, and the entire function of the bounded l-index on the set of variables

Bandura Andriy Ivanovych; Skaskiv Oleg Bogdanovich

Bandura Andriy Ivanovych ¹ , Skaskiv Oleg Bogdanovich ²

¹ Department of Physical and Mathematical Sciences, Ivano-Frankivsk National Technical University of Oil and Gas, Ivano-Frankivsk, 76019, Ukraine

² Department of theory of functions and functional analysis, Ivan Franko National University of Lviv, Lviv, 79000, Ukraine

Keywords: The Hier metric space, entire function

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Abstract

The metric properties of a space of entire functions of bounded L -index in joint variables are considered. It is proved that the space of entire functions is of the first category in the topology generated by Iyer’s metric. In the article, it is also proved existence theorem of a positive continuous vector-function L:Cⁿ → Rⁿ₊ for a given entire function F :Cⁿ→C with bounded multiplicities of its zero points such that F has bounded L-index in joint variables. This is a generalization of corresponding one-dimensional result.

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ACS Style: Bandura, A.I.; Skaskiv, O.B. The Hier metric space, the existence theorem, and the entire function of the bounded l-index on the set of variables. Bukovinian Mathematical Journal. 2018, 5
AMA Style: Bandura AI, Skaskiv OB. The Hier metric space, the existence theorem, and the entire function of the bounded l-index on the set of variables. Bukovinian Mathematical Journal. 2018; 5(3-4).
Chicago/Turabian Style: Andriy Ivanovych Bandura, Oleg Bogdanovich Skaskiv. 2018. "The Hier metric space, the existence theorem, and the entire function of the bounded l-index on the set of variables". Bukovinian Mathematical Journal. 5 no. 3-4.

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