ENDOMORPHISMS OF THE SPACE OF HIGHER-ORDER ENTIRE FUNCTIONS AND INFINITE-ORDER DIFFERENTIAL OPERATORS

• ISHIMURA Ryuichi

  Department of Mathematics and Informatics Faculty of Science, Chiba University

抄録

In this paper, we consider the space of entire functions for a given proximate order and a semi-norm, and show that a continuous endomorphism of this space is represented naturally as a partial differential operator of infinite order with entire function coefficients. Then, in the case of higher order, we study the relationship between the continuous endomorphisms and the linear partial differential operators of infinite order by means of the growth of the symbol of the operators.

収録刊行物

• 九州数学雑誌

  九州数学雑誌 61 (1), 83-94, 2007

  九州大学大学院数理学研究院

キーワード

• entire functions in several variables, partial differential operator of infinite order.

詳細情報

• CRID: 1390282680206406528
• NII論文ID: 130000063184
• NII書誌ID: AA10994346
• DOI: 10.2206/kyushujm.61.83
• ISSN: 18832032
• ISSN: 13406116
• MRID: 2317283
• Web Site: https://www.jstage.jst.go.jp/article/kyushujm/61/1/61_1_83/_pdf
• 本文言語コード: en
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