Researches on the structures of the spaces of analytic and harmonic functions and operators on them

• Project/Area Number: 24540190
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Basic analysis
• Research Institution: Nippon Institute of Technology
• Principal Investigator: OHNO Shuichi 日本工業大学, 工学部, 准教授 (20265367)
• Co-Investigator(Kenkyū-buntansha): IZUCHI Kei Ji 新潟大学, 自然科学系, フェロー (80120963) ; HOSOKAWA Takuya 茨城大学, 工学部, 准教授 (90553579)
• Project Period (FY): 2012-04-01 – 2015-03-31
• Project Status: Completed (Fiscal Year 2014)
• Budget Amount: ¥4,940,000 (Direct Cost: ¥3,800,000、Indirect Cost: ¥1,140,000); Fiscal Year 2014: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000); Fiscal Year 2013: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000); Fiscal Year 2012: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
• Keywords: 合成作用素 / 荷重合成作用素 / Hardy 空間 / Bergman 空間 / Bloch 空間 / Dirichlet空間 / 乗法作用素 / Hardy空間 / Bergman空間 / Bloch空間 / Besov空間

Outline of Final Research Achievements

The object of this research is to investigate the notion of ``compositions". It would be one of elementary and important problems to characterize the continuity (boundedness) and compactness of the ``composition".Our main purpose is to study the topological structure of ``compositions”.So we would like to estimate the difference of two different ``compositions”.

Research Products

• [Journal Article] Weighted composition operators on H∞・B_o. (2015)
  • Author(s): Shuichi Ohno
  • Journal Title: Glasgow Math. J. Volume: 57 Issue: 2 Pages: 475-480
  • DOI: 10.1017/s0017089514000469
  • Peer Reviewed / Open Access / Acknowledgement Compliant
• [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] Inner functions and weighted composition operators on the Hardy-Hilbert space with the unbounded weights (2015)
  • Author(s): Kei Ji Izuchi, Kou Hei Izuchi and Yuko Izuchi
  • Journal Title: Annals of Functional Analysis Volume: ６ Issue: 2 Pages: 104-115
  • DOI: 10.15352/afa/06-2-10
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Composition operators related to the Dirichlet space (2014)
  • Author(s): Shuichi Ohno
  • Journal Title: Bulletin of the Belgian Mathematical Society -- Simon Stevin Volume: ２１
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Topological structure of the space of weighted composition operators between different Hardy spaces (2014)
  • Author(s): Kei Ji Izuchi and Shuichi Ohno
  • Journal Title: Integral Equations Operator Theory Volume: ８０ Issue: 2 Pages: 153-164
  • DOI: 10.1007/s00020-014-2142-0
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Weighted composition operators on the minimal Mobius invariant space. (2014)
  • Author(s): Shuichi Ohno
  • Journal Title: Bull. Korean Math. Soc. Volume: 51 Issue: 4 Pages: 1187-1193
  • DOI: 10.4134/bkms.2014.51.4.1187
  • Peer Reviewed / Open Access / Acknowledgement Compliant
• [Journal Article] Some remarks on operator equation Cφ = CψX (2014)
  • Author(s): Takuya Hosokawa and Michio Seto
  • Journal Title: Nihonkai Mathematical Journal Volume: 25 Pages: 85-91
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Path connected components in weighted composition operators on h∞ and H ∞ with the essential operator norm (2014)
  • Author(s): Kei Ji Izuchi, Yuko Izuchi and Shuichi Ohno
  • Journal Title: Houston J. Math. Volume: 40
  • Peer Reviewed
• [Journal Article] Boundary vs. interior conditions associated with weighted composition operators (2014)
  • Author(s): Kei Ji Izuchi, Yuko Izuchi and Shuichi Ohno
  • Journal Title: Central Euro. J. Math. Volume: 12
  • Peer Reviewed
• [Journal Article] Interpolations for Holder's inequality (2013)
  • Author(s): Kei Ji Izuchi, Kou Hei Izuchi and Shuichi Ohno
  • Journal Title: Bull. Korean Math. Soc. Volume: 50 Issue: 3 Pages: 901-914
  • DOI: 10.4134/bkms.2013.50.3.901
  • Peer Reviewed
• [Journal Article] Path connected components in weighted composition operators on h∞ and H∞ with the operator norm (2013)
  • Author(s): Kei Ji Izuchi, Yuko Izuchi and Shuichi Ohno
  • Journal Title: Trans. Amer. Math. Soc. Volume: 365
  • Peer Reviewed
• [Journal Article] Mixed invariant subspaces over the bidisk II (2013)
  • Author(s): Kou Hei Izuchi and Kei Ji Izuchi
  • Journal Title: Acta Math. Vietnam Volume: 38 Issue: 2 Pages: 213-239
  • DOI: 10.1007/s40306-013-0016-1
  • Peer Reviewed
• [Journal Article] Ranks of backward shift invariant subspaces of the Hardy space over the bidisk (2013)
  • Author(s): Kei Ji Izuchi, Kou Hei Izuchi and Yuko Izuchi
  • Journal Title: Math. Z. Volume: 274 Issue: 3-4 Pages: 885-903
  • DOI: 10.1007/s00209-012-1100-2
  • Peer Reviewed
• [Journal Article] Gleason parts and countably generated closed ideals in H∞ (2013)
  • Author(s): Kei Ji Izuchi and Yuko Izuchi
  • Journal Title: Trans. Amer. Math. Soc. Volume: 365 Issue: 10 Pages: 5071-5083
  • DOI: 10.1090/s0002-9947-2013-05693-0
  • Peer Reviewed
• [Journal Article] On Mortini's question concerning the level sets on M(H∞) of a certain harmonic function (2013)
  • Author(s): Kei Ji Izuchi and Yuko Izuchi
  • Journal Title: Topology Appl. Volume: 160 Issue: 10 Pages: 1099-1101
  • DOI: 10.1016/j.topol.2013.04.014
  • Peer Reviewed
• [Journal Article] Essential norms of linear combinations of composition operators on h∞ (2013)
  • Author(s): Kei Ji Izuchi and Kou Hei Izuchi
  • Journal Title: J. Korean Math. Soc. Volume: 50 Issue: 1 Pages: 137-159
  • DOI: 10.4134/jkms.2013.50.1.137
  • Peer Reviewed
• [Journal Article] Non-analytic sets and QC-level sets in the maximal ideal space of H∞ (2013)
  • Author(s): Kei Ji Izuchi and Yuko Izuchi
  • Journal Title: Complex Var. Elliptic Equ. Volume: 58 Issue: 3 Pages: 317-332
  • DOI: 10.1080/17476933.2011.586695
  • Peer Reviewed
• [Journal Article] Sums of weighted composition operators on COP (2013)
  • Author(s): Kei Ji Izuchi, Kou Hei Izuchi and Yuko Izuchi
  • Journal Title: Glasgow Math. J. Volume: 55 Issue: 1 Pages: 229-239
  • DOI: 10.1017/s0017089512000511
  • Peer Reviewed
• [Journal Article] Composition operators induced by analytic maps to the polydisk (2012)
  • Author(s): Kei Ji Izuchi, Quang Dieu Nguyen and Shuichi Ohno
  • Journal Title: Canadian J. Math. Volume: 64 Issue: 6 Pages: 1329-1340
  • DOI: 10.4153/cjm-2011-073-3
  • Peer Reviewed
• [Journal Article] Differences of weighted composition operators from H∞ to Bloch space (2012)
  • Author(s): Takuya Hosokawa and Shuichi Ohno
  • Journal Title: Taiwanese J. Math. Volume: 16 Pages: 2093-2105
  • Peer Reviewed
• [Journal Article] Mutually prime sequences of inner functions and the ranks of subspaces over the bidisk (2012)
  • Author(s): Kei Ji Izuchi, Kou Hei Izuchi and Yuko Izuchi
  • Journal Title: Arch. Math. (Basel) Volume: 98 Issue: 6 Pages: 535-543
  • DOI: 10.1007/s00013-012-0394-y
  • Peer Reviewed
• [Journal Article] Wandering subspaces and the Beurling type theorem, III (2012)
  • Author(s): Kei Ji Izuchi, Kou Hei Izuchi and Yuko Izuchi
  • Journal Title: Journal of the Mathematical Society of Japan Volume: 64 Issue: 2 Pages: 627-658
  • DOI: 10.2969/jmsj/06420627
  • NAID: 10030740444
  • ISSN: 0025-5645, 1881-1167, 1881-2333
  • Peer Reviewed
• [Journal Article] Cross commutators on backward shift invariant subspaces over the bidisk II (2012)
  • Author(s): Kei Ji Izuchi and Kou Hei Izuchi
  • Journal Title: J. Korean Math. Soc. Volume: 49 Issue: 1 Pages: 139-151
  • DOI: 10.4134/jkms.2012.49.1.139
  • Peer Reviewed
• [Journal Article] Commutativity in two-variable Jordan blocks on the Hardy space (2012)
  • Author(s): Kei Ji Izuchi and Kou Hei Izuchi
  • Journal Title: Acta Sci. Math. (Szeged) Volume: 78 Pages: 129-136
  • Peer Reviewed
• [Presentation] Weighted composition operators on the minimal Mobius invariant space (2015)
  • Author(s): 大野修一
  • Organizer: 日本数学会年会
  • Place of Presentation: 明治大学(東京都千代田区)
  • Year and Date: 2015-03-21
• [Presentation] Topological structure of the space of weighted composition operators between different Hardy spaces (2014)
  • Author(s): 泉池 敬司, 大野修一
  • Organizer: 日本数学会秋季総合分科会
  • Place of Presentation: 広島大学(広島県東広島市)
  • Year and Date: 2014-09-27
• [Presentation] Composition operators related to the Dirichlet space (2014)
  • Author(s): 大野修一
  • Organizer: 日本数学会秋季総合分科会
  • Place of Presentation: 広島大学(広島県東広島市)
  • Year and Date: 2014-09-27
• [Presentation] Hankelness of composition operators (2014)
  • Author(s): 大野修一
  • Organizer: 第2回日立解析学セミナー
  • Place of Presentation: 茨城大学工学部(茨城県日立市)
  • Year and Date: 2014-07-18
• [Presentation] An operator equation of composition operators (2014)
  • Author(s): 細川 卓也
  • Organizer: 第2回日立解析学セミナー
  • Place of Presentation: 茨城大学工学部(茨城県日立市)
  • Year and Date: 2014-07-18
• [Presentation] Path connected components in the space of weighted composition operators on the disk algebra
  • Author(s): 泉池 敬司, 泉池 佑子, 大野修一
  • Organizer: 日本数学会年会, 函数解析学分科会
  • Place of Presentation: 学習院大学（東京都豊島区）
• [Presentation] Weighted Bergman spaces embedded in the Hardy space over the bidisk
  • Author(s): 泉池 敬司
  • Organizer: 関数環研究集会
  • Place of Presentation: クロスパスにいがた生涯学習センター（新潟県新潟市中央区）
• [Presentation] Linear combinations of composition operators on H∞ and the Bloch space
  • 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（東京都文京区）
• [Presentation] Differences of weighted composition operators from H∞ to the Bloch space
  • Author(s): 細川卓也, 大野修一
  • Organizer: 日本数学会秋季総合分科会，函数解析学分科会
  • Place of Presentation: 愛媛大学（愛媛県松山市）
• [Presentation] Composition operators induced by analytic maps to the polydisk
  • Author(s): 泉池 敬司, Quang Dieu Nguyen, 大野修一
  • Organizer: 日本数学会秋季総合分科会
  • Place of Presentation: 京都大学（京都府）
• [Presentation] Composition operators related to the Dirichlet space
  • Author(s): 大野修一
  • Organizer: 解析学セミナー
  • Place of Presentation: 新潟大学理学部（新潟県）
• [Presentation] An example of an invariant subspace M such that zM+wM is not closed
  • Author(s): 泉池 敬司
  • Organizer: 解析学セミナー
  • Place of Presentation: 新潟大学理学部（新潟県）
• [Presentation] Eigenfunctions of power compact weighted composition operators on H∞
  • Author(s): 細川卓也
  • Organizer: 解析学セミナー
  • Place of Presentation: 新潟大学理学部（新潟県）
• [Presentation] Some properties of composition operators
  • Author(s): 大野修一
  • Organizer: 日立解析学セミナー
  • Place of Presentation: 茨城大学工学部（茨城県）
• [Presentation] Composition operators between Hardy and Dirichlet spaces
  • Author(s): Shuichi Ohno
  • Organizer: The 22nd Miyashiro Seminar Complex Analysis and Operator Theory
  • Place of Presentation: 日本工業大学（埼玉県）
• [Presentation] Some notes on composition operators on the Bloch space
  • Author(s): 細川卓也
  • Organizer: 第２１回宮代セミナー
  • Place of Presentation: 日本工業大学（埼玉県）
• [Presentation] Interpolations for Holder’s inequality
  • Author(s): 泉池 敬司,泉池 耕平,大野修一
  • Organizer: 実解析学シンポジュウム2012
  • Place of Presentation: 茨城大学理学部（茨城県）
• [Presentation] Topological structure of the space of weighted composition operators on H∞
  • Author(s): 大野修一
  • Organizer: 日本数学会秋季総合分科会
  • Place of Presentation: 九州大学（福岡県）
  • Invited
• [Presentation] Sums of weighted composition operators on H∞
  • Author(s): 泉池 敬司,大野修一
  • Organizer: 日本数学会秋季総合分科会
  • Place of Presentation: 九州大学（福岡県）
• [Presentation] Differences of weighted composition operators from the Bloch space to H∞
  • Author(s): 細川 卓也, 大野修一
  • Organizer: 日本数学会秋季総合分科会
  • Place of Presentation: 九州大学（福岡県）
• [Presentation] Differences of weighted composition operators
  • Author(s): Takuya Hosokawa
  • Organizer: Functional Analysis Seminar
  • Place of Presentation: Helsinki University(フィンランド)
• [Presentation] Ranks of invariant and backward shift invariant subspaces of the Hardy space over the bidisk
  • Author(s): Kei Ji Izuchi
  • Organizer: Topology and Functional Analysis
  • Place of Presentation: Fudan University(中国)
  • Invited