Spectral and inverse scattering theory on non-compact manifolds

• Project/Area Number: 21340028
• Research Category: Grant-in-Aid for Scientific Research (B)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Basic analysis
• Research Institution: University of Tsukuba
• Principal Investigator: ISOZAKI Hiroshi 筑波大学, 数理物質系, 教授 (90111913)
• Project Period (FY): 2009 – 2012
• Project Status: Completed (Fiscal Year 2012)
• Budget Amount: ¥16,380,000 (Direct Cost: ¥12,600,000、Indirect Cost: ¥3,780,000); Fiscal Year 2012: ¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000); Fiscal Year 2011: ¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000); Fiscal Year 2010: ¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000); Fiscal Year 2009: ¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
• Keywords: スペクトル理論 / 逆問題 / 散乱理論 / S行列 / ディリクレ・ノイマン写像 / Ｓ行列 / ディリクレノイマン写像 / 非コンパクト多様体 / リーマン計量 / ラプラス-ベルトラミ作用素 / 波動方程式 / 境界制御法 / 多様体 / DN写像

Research Abstract

(1) The inverse scattering from cusp on asymptotically hyperbolic manifolds with conical singularities.
(2) The reconstruction of the potential from the S-matrix of one fixed energy for the discrete Schroedinger operator on square lattice as well as the Rellich type uniqueness theorem.
(3) The reconstruction of discontinuities of heat conductivity from the local boundary measurements, with numerical computation.

Research Products

• [Journal Article] Proving for heat conductive bodies (2012)
  • Author(s): P.Gaitan, H.Isozaki, O.Poisson, S.Siltanen and J.Tamminenn
  • Journal Title: Inverse Problems and Imaging Volume: 6 Issue: 3 Pages: 423-446
  • DOI: 10.3934/ipi.2012.6.423
  • Peer Reviewed
• [Journal Article] On the wave operators for the Friedrichs-Faddeev model (2012)
  • Author(s): H.Isozaki and S.Richard
  • Journal Title: Ann. Henri Poincare Volume: 13 Issue: 6 Pages: 1469-1482
  • DOI: 10.1007/s00023-012-0161-4
  • Peer Reviewed
• [Journal Article] Inverse problems, trace formula for discrete Schroedinger operators (2012)
  • Author(s): H.Isozaki and E.Korotyaev
  • Journal Title: Ann. Henri Poincare Volume: 13 Issue: 4 Pages: 751-788
  • DOI: 10.1007/s00023-011-0141-0
  • Peer Reviewed
• [Journal Article] Gauge equivalence and inverse scattering for long-range magnetic potentials (2010)
  • Author(s): G. Eskin and H. Isozaki
  • Journal Title: Russian J. of Math. Phys Volume: Vol 18, No 1 Issue: 1 Pages: 19-28
  • DOI: 10.1134/s1061920811010067
  • Peer Reviewed
• [Journal Article] Gauge equivalence and inverse scattering for Ahoronov-Bohm effect (2010)
  • Author(s): G. Eskin, H. Isozaki and S. O'dell
  • Journal Title: Commun. in P. D. E. Volume: 35 Issue: 12 Pages: 1-31
  • DOI: 10.1080/03605301003758344
  • Peer Reviewed
• [Journal Article] Spectral theory and inverse problems on asymptotically hyperbolic manifolds (2010)
  • Author(s): H. Isozaki and Y. Kurylev
  • Journal Title: RIMS Kokyuroku Bessatsu Volume: B16 Pages: 29-73
  • URL: http://www.kurism.kyoto-u.ac.jp/~kenkyubu/bessatsu.html
  • Peer Reviewed
• [Journal Article] Forward and inverse scattering problem on manifolds with asymptotically cylindrical ends (2010)
  • Author(s): H.Isozaki, Y.Kurylev and M.Lassas
  • Journal Title: Journal of Funct. Anal. Volume: 258 Pages: 2060-2118
  • URL: http://dx.doi.org/10.1016/j.jfa.2009.11.669
  • Peer Reviewed
• [Journal Article] Local detection of three-dimensional inclusions in electrical impedance tomography (2010)
  • Author(s): T.Ide, H.Isozaki, S.Nakata and S.Siltanen
  • Journal Title: Inverse Problems Volume: 26 No. 3 Pages: 35001-35001
  • NAID: 120007138215
  • Peer Reviewed
• [Journal Article] Local detection of three-dimensional inclusions in electrical impedance tomography (2010)
  • Author(s): T.Ide, H.Isozaki, S.Nakata, S.Siltanen
  • Journal Title: Inverse ProbLems Volume: 26
  • NAID: 120007138215
  • Peer Reviewed
• [Journal Article] Gauge equivalence , inverse scattering for Ahoronov-Bohm effect (2010)
  • Author(s): G.Eskin, H.Isozaki , S.odel
  • Journal Title: Comm.In P.D.E. Volume: 35 Pages: 1-31
  • Peer Reviewed
• [Journal Article] Forward , inverse scattering problem on manifolds with asympt tically cylindrical ends (2010)
  • Author(s): H.Isozaki, Y.Kurylev, M.Lassas
  • Journal Title: Journal of Functional Analysis Volume: 258 Pages: 2060-2118
• [Journal Article] Spectral theory , inverse problems on asymptotically hyperboliac manifold (2010)
  • Author(s): H.Isozaki , Y.Kurylev
  • Journal Title: RIMS Kokyuroku Bessatsu Volume: B16 Pages: 29-73
  • Peer Reviewed
• [Journal Article] Gauge equivalence , inverse scattering for long-range magnetic potentials (2010)
  • Author(s): G.Eskin, H.Isozaki
  • Journal Title: Russian Journal of Mathematical Physics Volume: 18 Pages: 19-28
  • Peer Reviewed
• [Journal Article] Pseudodifferential multi-product representation of the solution operator of a parabolic equation (2009)
  • Author(s): H.Isozaki, J.Le Rousseau
  • Journal Title: Comm.in P.D.E. 34 Pages: 625-655
  • NAID: 120007137999
  • Peer Reviewed
• [Presentation] Spectral theory and inverse problems for discrete Schroedinger operators (2012)
  • Author(s): 磯崎洋
  • Organizer: Taiwan-Japan joint conference on PDE and Analysis
  • Place of Presentation: 台湾大学, 台湾
  • Year and Date: 2012-12-26
• [Presentation] Inverse scattering for discrete Schroedinger operators (2012)
  • Author(s): 磯崎洋
  • Organizer: Seminaire d'EDP
  • Place of Presentation: Rennes大学, フランス
  • Year and Date: 2012-12-06
• [Presentation] Inverse scattering for discrete Schroedinger operators (2012)
  • Author(s): 磯崎洋
  • Organizer: Inverse problems and applications
  • Place of Presentation: Hangzhou, 中国
  • Year and Date: 2012-09-19
• [Presentation] Inverse scattering at a fixed energy for discrete Schroedinger operators on the square lattice (2012)
  • Author(s): 磯崎洋
  • Organizer: 日本数学会秋季総合分科会
  • Place of Presentation: 九州大学
  • Year and Date: 2012-09-18
• [Presentation] A Rellich type theorem for discrete Schroedinger operators (2012)
  • Author(s): 磯崎洋, 森岡悠
  • Organizer: 日本数学会秋季総合分科会
  • Place of Presentation: 九州大学
  • Year and Date: 2012-09-18
• [Presentation] Inverse problems for heat equations with discontinuous conductivities (2012)
  • Author(s): H.Isozaki
  • Organizer: Recent challenges of Mathematics in Oncology and Biology of Cancer
  • Place of Presentation: Centre International de Rencontre de Mathematique (France, Marseille)(招待講演)
  • Year and Date: 2012-03-22
• [Presentation] Inverse scattering on generalized arithmetic surfaces (2012)
  • Author(s): 磯崎洋, 森岡悠
  • Organizer: Geometric analysis on Euclidean and homogeneous spaces
  • Place of Presentation: Tufts University, 米国
  • Year and Date: 2012-01-09
• [Presentation] Inverse scattering on a generalized arithmetic surfaces (2012)
  • Author(s): H.Isozaki
  • Organizer: Workshop Geometric analysis on Euclidean and homogeneous spaces
  • Place of Presentation: Tufts University (USA, Boston)(招待講演)
  • Year and Date: 2012-01-09
• [Presentation] Introduction to the spectral theory on generalized arithmetic surfaces (2011)
  • Author(s): 磯崎洋
  • Organizer: Inverse Days
  • Place of Presentation: University of Helsinki, フィンランド
  • Year and Date: 2011-12-16
• [Presentation] Introduction to the spectral theory on generalized arithmetic surface (2011)
  • Author(s): H.Isozaki
  • Organizer: Inverse Days
  • Place of Presentation: University of Helsinki(Finland, Helsinki)(招待講演)
  • Year and Date: 2011-12-16
• [Presentation] Inverse scattering for discreteSchroedinger operators (2011)
  • Author(s): 磯崎洋
  • Organizer: ロンドン解析セミナー
  • Place of Presentation: ロンドン大学, 英国
  • Year and Date: 2011-10-27
• [Presentation] Inverse scattering on generalized arithmetic surfaces (2011)
  • Author(s): 磯崎洋
  • Organizer: 金沢大学談話会
  • Place of Presentation: 金沢大学
  • Year and Date: 2011-10-17
• [Presentation] 尖点・錘状特異点を持つ漸近的2次元双曲多様体上の逆散乱問題 (2011)
  • Author(s): 磯崎洋
  • Organizer: 日本数学会秋季総合分科会
  • Place of Presentation: 信州大学
  • Year and Date: 2011-09-29
• [Presentation] 尖点・錘状特異点を持つ漸近的2次元双曲多様体上の逆散乱問題 (2011)
  • Author(s): 磯崎洋
  • Organizer: 日本数学会秋季総合分科会
  • Place of Presentation: 信州大学(松本市)
  • Year and Date: 2011-09-29
• [Presentation] Inverse Problems in Analysis and Geometry (2011)
  • Author(s): 磯崎洋
  • Organizer: Issac Newton Institute
  • Place of Presentation: 英国
  • Year and Date: 2011-08-05
• [Presentation] Inverse scattering from cusp on generalized arithmetic surfaces (2011)
  • Author(s): H.Isozaki
  • Organizer: Inverse Problems in Analysis and Geometry
  • Place of Presentation: Issac Newton Institute (UK, Cambridge)(招待講演)
  • Year and Date: 2011-08-05
• [Presentation] Inverse scattering from cusp (2010)
  • Author(s): 磯崎洋
  • Organizer: Workshop on Inverse problems : Theory and applications, MSRI
  • Place of Presentation: 米国
  • Year and Date: 2010-11-10
• [Presentation] Inverse scattering from cusp (2010)
  • Author(s): 磯崎洋
  • Organizer: MSRI Workshop on Inverse Problems
  • Place of Presentation: Mathematical Science Research Institute(Berkeley),USA(招待講演)
  • Year and Date: 2010-11-10
• [Presentation] Inverse scattering from cusp (2010)
  • Author(s): 磯崎洋
  • Organizer: UCLA Dept. of Math. Colloquium talk
  • Place of Presentation: カリフォルニア大学, 米国
  • Year and Date: 2010-11-04
• [Presentation] Inverse scattering from cusp (2010)
  • Author(s): 磯崎洋
  • Organizer: UCLA Faculty colloquium
  • Place of Presentation: カリフォルニア大学ロサンゼルス校 USA
  • Year and Date: 2010-11-04
• [Presentation] 3次元における局所化されたデータからの包含物の数値実験 (2010)
  • Author(s): 仲田晋、磯崎洋、井手貴範、Samuli Siltanen
  • Organizer: 日本応用数理学会
  • Place of Presentation: 明治大学
  • Year and Date: 2010-09-09
• [Presentation] Inverse scattering on non-compact manifolds (2010)
  • Author(s): 磯崎洋
  • Organizer: AIP Conference
  • Place of Presentation: Wien 大学, オーストリア
  • Year and Date: 2010-07-20
• [Presentation] リーマン面と逆散乱問題 (2010)
  • Author(s): 磯崎洋
  • Organizer: 筑波大学微分幾何セミナー
  • Place of Presentation: 筑波大学
  • Year and Date: 2010-05-25
• [Presentation] リーマン面上での逆散乱問題 (2010)
  • Author(s): 磯崎洋
  • Organizer: 偏微分方程式松山キャンプ
  • Place of Presentation: 愛媛大学
  • Year and Date: 2010-01-06
• [Presentation] リーマン面上での逆散乱問題 (2010)
  • Author(s): 磯崎洋
  • Organizer: 微分方程式松山キャンプ
  • Place of Presentation: 愛媛大学
  • Year and Date: 2010-01-06
• [Presentation] リーマン面上での逆散乱問題 (2009)
  • Author(s): 磯崎洋
  • Organizer: 浜松偏微分方程式セミナー
  • Place of Presentation: 静岡大学
  • Year and Date: 2009-12-21
• [Presentation] Inverse scattering from cuspParis-London Analysis Seminar (2009)
  • Author(s): 磯崎洋
  • Organizer: L'Institute Henri Poincare
  • Place of Presentation: フランス
  • Year and Date: 2009-12-04
• [Presentation] Inverse scattering from cusp (2009)
  • Author(s): 磯崎洋
  • Organizer: Paris-London analysis seminar
  • Place of Presentation: Henri Poincare研究所,フランス
  • Year and Date: 2009-12-04
• [Presentation] EIT における3次元数値計算-局所化されたデータからの包含物の同定 (2009)
  • Author(s): 磯崎洋
  • Organizer: 日本数学会秋季総合分科会
  • Place of Presentation: 大阪大学
  • Year and Date: 2009-09-27
• [Presentation] Waveguide に関する逆散乱問題 (2009)
  • Author(s): 磯崎洋
  • Organizer: 日本数学会秋季総合分科会
  • Place of Presentation: 大阪大学
  • Year and Date: 2009-09-27
• [Presentation] 漸近的双曲計量に関する逆散乱問題 (2009)
  • Author(s): 磯崎洋
  • Organizer: 日本数学会秋季総合分科会
  • Place of Presentation: 大阪大学
  • Year and Date: 2009-09-27
• [Presentation] EIT年おける3次元数値計算-局所化されたデータからの包含物の同定- (2009)
  • Author(s): 磯崎洋
  • Organizer: 日本数学会秋季総合分科会
  • Place of Presentation: 大阪大学
  • Year and Date: 2009-09-27
• [Presentation] 漸近的双曲計量に関する逆散乱問題、Waveguideに関する逆散乱問題 (2009)
  • Author(s): 磯崎洋
  • Organizer: 日本数学会秋季総合分科会
  • Place of Presentation: 大阪大学
  • Year and Date: 2009-09-24
• [Presentation] Inverse scattering on non-compact manifolds (2009)
  • Author(s): 磯崎洋
  • Organizer: Applied Inverse Problem Conference
  • Place of Presentation: Wien大学、オーストムア
  • Year and Date: 2009-07-20
• [Presentation] 非コンパクト多様体上の逆散乱問題 (2009)
  • Author(s): 磯崎洋
  • Organizer: 神戸大学談話会
  • Place of Presentation: 神戸大学
  • Year and Date: 2009-07-01
• [Presentation] 多様体上のフーリエ変換、ラドン変換と波動方程式 (2009)
  • Author(s): 磯崎洋
  • Organizer: Encounter with Mathematics
  • Place of Presentation: 中央大学
  • Year and Date: 2009-05-30
• [Presentation] Inverse scattering for discrete Schroedinger operators
  • Author(s): 磯崎 洋
  • Organizer: Inverse Problems and Applications
  • Place of Presentation: Hangzhou, China
  • Invited
• [Presentation] A Rellich type theorem for discrete Schroedinger operators
  • Author(s): 森岡 悠
  • Organizer: 日本数学会秋季総合分科会
  • Place of Presentation: 九州大学
• [Presentation] Inverse scattering at a fixed energy for discrete Schroedinger operators on the square lattice
  • Author(s): 森岡 悠
  • Organizer: 日本数学会秋季総合分科会
  • Place of Presentation: 九州大学
• [Presentation] Inverse scattering for discrete Schroedinger operators
  • Author(s): 磯崎 洋
  • Organizer: Seminaire d’EDP
  • Place of Presentation: Ｒｅｎｎｅ大学, フランス
• [Presentation] Spectral theory and inverse problems for discrete Schroedinger operators
  • Author(s): 磯崎 洋
  • Organizer: Taiwan-Japan joint conference on PDE and analysis
  • Place of Presentation: 台湾大学、台湾
• [Book] 超関数・フーリエ変換入門 (2010)
  • Author(s): 磯崎洋
  • Total Pages: 151
  • Publisher: サイエンス社
• [Book] 超関数・フーリエ変換入門 基礎から偏微分方程式への応用まで (2009)
  • Author(s): 磯崎洋
  • Total Pages: 151
  • Publisher: サイエンス社