Hiroshima Mathematical Journal

The spaces of formal power series of class M of Roumieu type and of Beurling type

Xiaoran Jin

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Abstract

In this article, we introduce the space of formal power series of class $\mathbb M$ of Roumieu (resp., Beurling) type, which is the generalization of the space of entire functions of normal (resp., minimal) type with respect to a proximate order. And we characterize continuous endomorphisms of these spaces.

Note

Dedicate to Professor R. Ishimura

Article information

Source
Hiroshima Math. J., Volume 50, Number 1 (2020), 117-135.

Dates
Received: 7 March 2019
Revised: 8 August 2019
First available in Project Euclid: 10 March 2020

Permanent link to this document
https://projecteuclid.org/euclid.hmj/1583805652

Digital Object Identifier
doi:10.32917/hmj/1583805652

Mathematical Reviews number (MathSciNet)
MR4074382

Zentralblatt MATH identifier
07197873

Subjects
Primary: 32A05: Power series, series of functions
Secondary: 32A15: Entire functions 30D15: Special classes of entire functions and growth estimates

Keywords
formal power seires Roumieu type Beurling type

Citation

Jin, Xiaoran. The spaces of formal power series of class M of Roumieu type and of Beurling type. Hiroshima Math. J. 50 (2020), no. 1, 117--135. doi:10.32917/hmj/1583805652. https://projecteuclid.org/euclid.hmj/1583805652


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