Study on topological structure of multiplication and composition of analytic functions

• Project/Area Number: 25800055
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Basic analysis
• Research Institution: Ibaraki University
• Principal Investigator: Hosokawa Takuya 茨城大学, 工学部, 准教授 (90553579)
• Project Period (FY): 2013-04-01 – 2016-03-31
• Project Status: Completed (Fiscal Year 2015)
• Budget Amount: ¥3,120,000 (Direct Cost: ¥2,400,000、Indirect Cost: ¥720,000); Fiscal Year 2015: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2014: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2013: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
• Keywords: 合成作用素 / 加重合成作用素 / 解析関数空間 / 函数解析学 / 複素解析学 / 荷重合成作用素 / 関数解析学 / 荷重付き合成作用素

Outline of Final Research Achievements

(1) We characterized the Hilbert-Schmidt properties of the differences of two composition operators between some Hilbert spaces of analytic functions by the conditions on the integrals of their symbol functions.
(2) We solved a certain operator equation of composition operators on Hardy space.
(3) We characterized the compactness of composition operators induced by the product of two analytic self-maps on Bergman space by the boundary behavior of those analytic self-maps.

Research Products

• [Journal Article] Weighted composition operators between Hilbert spaces of analytic functions in the operator norm and Hilbert-Schmidt norm topologies (2015)
  • Author(s): T. Hosokawa, K. Izuchi, S. Ohno
  • Journal Title: J. Math. Anal. Appl. Volume: 421 Issue: 2 Pages: 1546-1558
  • DOI: 10.1016/j.jmaa.2014.07.043
  • Peer Reviewed
• [Journal Article] Some remarks on operator equation C_φ = C_ψ X (2014)
  • Author(s): Takuya Hosokawa and Michio Seto
  • Journal Title: Nihonkai Math. J. Volume: 25 Pages: 85-91
  • Peer Reviewed
• [Presentation] 単位円板上の正則自己写像の積と合成作用素の性質について (2016)
  • Author(s): 細川卓也
  • Organizer: つくばセミナー
  • Place of Presentation: 筑波大学 自然系学系棟Ｄ８１４
  • Year and Date: 2016-03-08
• [Presentation] Composition operators with product symbols (2015)
  • Author(s): 細川卓也
  • Organizer: ２０１５年度 関数 環研究集会
  • Place of Presentation: 新潟大学駅南キャンパス「ときめいと」
  • Year and Date: 2015-12-19
• [Presentation] Weighted composition operators between Hilbert spaces of analytic functions in Hilbert-Schmidt norm topologies (2015)
  • Author(s): 細川卓也
  • Organizer: 日本数学会２０１５年度秋季総合分科会
  • Place of Presentation: 京都産業大学
  • Year and Date: 2015-09-15
• [Presentation] Differences of weighted composition operators from H∞ to the Bloch space (2013)
  • Author(s): 細川卓也
  • Organizer: 2013日本数学会秋季総合分科会
  • Place of Presentation: 愛媛大学城北キャンパス
• [Presentation] Linear combinations of composition operators on H∞ and the Bloch space (2013)
  • Author(s): 細川卓也
  • Organizer: ２０１３年作用素論・作用素環論研究集会
  • Place of Presentation: お茶の水女子大学
  • Invited