函数解析学と実解析学の融合的研究

1997 年度 実績報告書

• 研究課題/領域番号: 09304018
• 研究種目: 基盤研究(A)
• 研究機関: 東京理科大学
• 研究代表者: 大矢 雅則 東京理科大学, 理工学部, 教授 (90112896)
• 研究分担者: 田島 慎一 新潟大学, 工学部, 助教授 (70155076) ; 辛崎 秀樹 九州大学, 大学院数理学研究科, 教授 (20186612) ; 竹中 茂夫 岡山理科大学, 理学部, 教授 (80022680) ; 佐藤 亮太郎 岡山大学, 理学部, 教授 (50077913)
• キーワード: 函数解析 / 実解析 / 実函数論 / 量子数理 / 表現論と調和解析 / 作用素環・函数環 / 作用素 / 偏微分方程式

研究概要

本研究では,その研究対象により5つの研究グループに分かれ各研究グループでの活動を行い,さらに,本研究全体の方向付けと取りまとめを行うために全体として合同シンポジウムの開催と合同打合会を行った.合同シンポジウムは7月22日から7月24日茨城大学茨苑会館(講演者数10)で行われ,各研究グループから選ばれた講演者が最近の函数解析や実解析学の話題を報告した(図書1).合同打合会は日本数学会年会(春),同(秋),合同シンポジウムの時期に合わせて合計年3回,各研究グループの代表が参加して行われた.また,5つの研究グループは各グループ毎にいくつかの研究集会を主催し研究成果の発表を行った(図書2,3,4,5,6).
実解析グループでは実函数論,確率論,函数解析学等の幅広い分野にわたって研究が行われ,興味あるいくつかの成果を得た.量子数理と作用素のグループでは量子情報理論をベースとした量子通信効率(誤り確率,通信路容量など)の研究及びそれらの量子コンピュータ,量子カオス理論への適用に関する研究や作用素に関わる不等式や線形非線形作用素論から自由境界問題,関連する力学系の安定性等に関する研究が行われた.表現論と調和解析の研究では連続群とくにリー群の無限次元表現の理論を通して一般調和解析学の他分野との関連が研究された.作用素環・函数環の研究グループでは部分因子環から生じる不変量の詳しい考察や作用素環と関係するある種のエントロピー,力学系の研究等が行われた.偏微分方程式の函数解析的研究グループでは実解析と関数解析学の理論・手法に基づいて種々の偏微分方程式系を解析し,さらにそれらの成果の数学の他分野や情報数理工学等への応用が行われた.

研究成果

• [文献書誌] M.Ohya: "Complexity,fractal dimension for quantum states" Open systems and Information Dynamics. 4. 141-157 (1997)
• [文献書誌] L.Accardi, M.Ohya and N.Watanabe: "Dynamical entropy through quantum Markov chains" Open systems and Information Dynamics. 4. 71-87 (1997)
• [文献書誌] 大矢雅則, 須鎗弘樹, 古市茂: "スクイズド真空状態による誤り確率の改善" 電子情報通信学会論文誌. 180-A,No.5. 809-817 (1997)
• [文献書誌] 大矢雅則, 須鎗弘樹, 樋口慶: "対称コンタクトプロセスによる二義錯視図形の解析" 電子情報通信学会論文誌. 180-A,No.6. 1022-1029 (1997)
• [文献書誌] M.Ohya, D.Petz and N.Watanabe: "On capacities of quantum channels" Probability and Mathematical Statistics. 17. 179-196 (1997)
• [文献書誌] S.Furuichi, M.Ohya and H.Suyari: "Computation of mutual entropy in quantum amplifier processes" Quantum Communication,Computing,and Measurement. 147-155 (1997)
• [文献書誌] M.Ohya and N.Watanabe: "Quantum capacity of noisy quantum channel" Quantum Communication,Computing,and Measurement. 213-220 (1997)
• [文献書誌] M.Ohya: "Complexities and their applications to characterization of chaos" to appear in International Journal of Theoretical Physics.
• [文献書誌] M.Ohya, D.Petz and N.Watanabe: "Numerical computation of quantum capacity" to appear in International Journal of Theoretical Phyasics.
• [文献書誌] M.Ohya and N.Watanabe: "On mathematical treatment of Fredkin-Toffoli-Milburn gate" to appear in Physica D.
• [文献書誌] K.Inoue, M.Ohya and H.Suyari: "Characterization of quantum teleportation processes by nonlinear quantum channel and quantum mutual entropy" to appear in Physica D.
• [文献書誌] N.Kenmochi and A.Damlamian: "Evolution equations associated with non-isothermal phase transitions" Functional Analysis and Global Analysis. 62-77 (1997)
• [文献書誌] N.Kenmochi, A.Ito and N.Yamazaki: "Global attractors of time-dependent double obstacle problems" Functional Analysis and Global Analysis. 288-301 (1997)
• [文献書誌] N.Kenmochi, A.Ito: "Asymptotic behaviour of solutions to non-isothermal phase separation model with constraints in one-dimensional space" to appear in J.Math.Soc.Japan.
• [文献書誌] N.Kenmochi, A.Ito and N.Yamazaki: "Attractors of nonlinear evolution systems generated by time-dependent subdifferentials in Hilbert spaces" to appear in Lecture Notes Pure Appl.Math.
• [文献書誌] N.Kenmochi, T.Koyama: "Parabolic PDE´s with hysteresis and quasivariational inequalities" to appear in Nonlinear Anal.TMA.
• [文献書誌] N.Kennmochi and A.Damlamian: "Evolution equations associated with non-isothermal phase separation:Subdifferential approach" to appear in Ann.Mat.Pura Appl.
• [文献書誌] N.Kennmochi, K.Shirakawa, A.Ito and N.Yamazaki: "Asymptotic stability for evolution equations governed by subdifferentials" to appear in Gakuto Intern.Ser.Math.Sci.Appl.11. (1997)
• [文献書誌] T.Ando and K.Okubo: "Holder type inequalities associated with operator radii and Schur products" Linear and Multilinear Algebra. 43. 53-61 (1997)
• [文献書誌] M.Fujii and N.Nakamura: "An application of operator means arising from a study on Wazan" Math.Japon. 46. 385-386 (1997)
• [文献書誌] T.Furuta: "Equivalence relations among Reid,Lοwner-Heinz and Heinz-Kato inequalities,and extensions of these inequalities" Integral equations and Operator Theory. 29. 1-9 (1997)
• [文献書誌] K.Izuchi and S.Takagasi: "BKW-oparators on the interval" Rend.circ,Mat.Palcrmo (2). 46. 477-489 (1997)
• [文献書誌] E.Kamei: "Complements to the Furuta inequality,II" Math.Japon. 45(1). 15-23 (1997)
• [文献書誌] M.Kato and T.Takahashi: "On the von Neumann-Jordan constants to Banach spaces" Proc.Amer.Math.soc. 125. 1055-1062 (1997)
• [文献書誌] T.Nakazi: "The commutator ideal in Toeplitz algebras for uniform algebras and the analytic structure" Arch Math.69. 221-226 (1997)
• [文献書誌] S.Takahasi and O.Hatori: "A structure of ring homomorphidmd on commutative Banach alegebras" to appear in Proc.Amer.Math.Soc.
• [文献書誌] T.Ando and F.Hiai: "Hοlder type inequalities for matrices" to appear in Math.Ineq.Appl.
• [文献書誌] M.Choda and T.Natsume: "Reduced C'-crossed products by free shifts" to appear in Ergod,Th.and Dynam.Sys.
• [文献書誌] M.Fujii, F.Jiang,and E.Kamei: "Characterization of chaotic order and its application to Furuta inequality" to appear in Proc.Amer.Math.Soc.
• [文献書誌] Y.Gotoh: "On global integrability of BMO functions on general domains" to appear in J.Anal.Math.
• [文献書誌] O.Hatori and K.Izuchi: "Apostol algebras and decomposition in Douglas algebras" to appear in Michigan Math.J.
• [文献書誌] M.Hayashi and T.Kato: "Point separation of a two-sheeted disc by bounded analytic functions" to appear in Hokkaido Math.J.
• [文献書誌] F.Hiai: "Standard invariants for crossed products inclusions of factors" Pacific J.Math.177. 237-267 (1997)
• [文献書誌] F.Hiai and M.Izumi: "Amenability and strong amenability for fusion algebras with applications to subfactors" to appear in Internat.J.Math.
• [文献書誌] Y.Iida and N.Mochizuki: "Isometries of some F-algebras of holomorphic functions" to appear in Arch. Math.
• [文献書誌] K.Izuchi: "Sequential type Korovkin theorem on 1^∞ for QC-test functions" Proc.Amer.Math.Soc.125. 1153-1159 (1997)
• [文献書誌] K.Izuchi and Y.Matsugu: "A^φ invariant subspaces on the torus" to appear in Canad.J.Math.
• [文献書誌] K.Izuchi and S.Ohno: "Selfadjoint commutators and invariant subspaces on the torus II" Integral Eq.Op.Th.27. 208-220 (1997)
• [文献書誌] M.Izumi: "Subalgebras of infinite C^*-lagebras with finite Watatani indices:II.Cuntz-Krieger algebras" to appear in Duke Math.J.
• [文献書誌] T.Kajiwara, C.Pinzari and Y.Watatani: "Ideal structure and simplicity of the C^*-algebras generated by Hilbert bimodules" to appear in J.Funct.Anal.
• [文献書誌] Y.Katayama, K.Matsumoto and Y.Watatani: "Simple C^*-algebras arizing from β-expansion of real numbers" to appear in Ergod.Th.and Dynam.Sys.
• [文献書誌] Y.Kawahigashi: "Classification of approximately inner automorphisms of subfactors" Math.Ann.308. 425-438 (1997)
• [文献書誌] S.Kawamura: "Covariant representations associated with chaotic dynamical systems" Tokyo J.Math.20. 205-217 (1997)
• [文献書誌] H.Kosaki, A.Munemasa,and S.Yamagami: "On fusion algebras associated to finite group actions" Pacific J.Math.177. 269-290 (1997)
• [文献書誌] H.Kurose and Y.Nakagami: "Compact Hopf *-algebras quantum enveloping algebras and dual Woronowicz algebras for quantum Lorentz groups" to appear in Internat.J.Math.
• [文献書誌] T.Nakazi and Y.Watatani: "Invariant subspace theorems for subdiagonal algebras" J.Operator Theory. 37. 379-395 (1997)
• [文献書誌] T.Kobayashi: "Discrete decomponsability of the restriction of Aq(λ) with respect to reductive subgroups II--microlocal analysis and asymptotic K-support" to appear in Annals of Math.
• [文献書誌] T.Kobayashi: "Discrete decomponsability of the restriction of Aq(λ) with respect to reductive subgroups III--restriction of Harish-Chandra modules and associated varieties" to appear in Invent.Math.
• [文献書誌] T.Kobayashi: "Discrete series representations for the orbit spaces arising from two involutions of real reductive Lie groups" to appear in J.Funct.Anal.
• [文献書誌] K.Nishiyama: "Redyctuve dual pair and Weil representation" Proceding of Summer School on Number Theorey. 63-88 (1997)
• [文献書誌] T.Umeda: "Newton's formula for gl_n" to appear in Proc.Amer.Math.Soc.
• [文献書誌] T.Nakajima and H.F.Yamda: "On reduced Q-functions" Hiroshima M.J.27. 407-414 (1997)
• [文献書誌] T.Tanisaki and S.-J.Kang: "Universal R-matrices and the center of the quantum generalized Kac-Moody algebras" Hiroshima Mathematical Journal.27・2. 347-360 (1997)
• [文献書誌] K.Hasegawa: "Ruijsenaars' commuting differnce operators as commuting transfer matrices" Comm.Math.Phys.187. 289-325 (1997)
• [文献書誌] A.Antonov, K.Hasegawa and A.Zabrodin: "On trigonometric intertwining vectors and non-dynamical R-matrix for the Ruijsenaars model" Nuclear Physics B. 503. 747-770 (1997)
• [文献書誌] K.Kumahara: "On non-unitary induced representations of a generalized Heisenberg group" Mathematica Japonica. 46. 5-14 (1997)
• [文献書誌] K.Kikuchi: "K-spherical representations for Gelfand pairs associated to solvable Lie groups" J.Math.Soc.Japan. 49. 469-486 (1997)
• [文献書誌] T.Hashimoto: "Integrability of one-parameter groups generated by the Virasoro operators" J.Funct.Anal.149. 178-199 (1997)
• [文献書誌] T.Kobayashi: "Invariant measures on homogeneous manifolds of reductive type" J.reine und angew.Math.490. 37-53 (1997)
• [文献書誌] T.Aoki: "Multiple-scale analysis for Painleve´ transcendents with a large parameter" Differential Geometry and Mathmatical Physics. 39. 11-17 (1997)
• [文献書誌] A.Arai: "A class of representations of the *-algebra of the canonical commutation relations over a Hilbert space and instability of embedded eigenvalues in quantum field models" J.Nonlinear Math.Phys.4. 338-349 (1997)
• [文献書誌] K.Fujita and M.Morimoto: "Spherical Fourier-Borel transformation" Functional analysis and global analysis. 78-87 (1997)
• [文献書誌] T.Hishida: "On a class of stable steady flows to the exterior convection problem" Journal of Differential Equations. 140.
• [文献書誌] T.Ichinose and T.Satoshi: "Estimate of the difference between the Kac operator and the Schrodinger semigroup" Commun.Math.Phys.186. (1997)
• [文献書誌] Y.Ito: "Theory of Fourier microfunctions of several types (III)" to appear in Journal of Mathematics,Tokushima University. 31. 29-61 (1997)
• [文献書誌] T.Kako and L.Deng: "Finite element approximation of eigenvalue problem for a coupled vibration berween acoustic field and plate" J.Comput.Math.15・3. 265-278 (1997)
• [文献書誌] J.Kamimoto: "Singularities of the Bergman kernel for certain weakly pseudoconvex domains" to appear in Journal of Mathematical Sciences,the University of Tokyo.
• [文献書誌] T.Kawai and H.P.Stapp: "On infrared singularities" New Trends in Microlocal Analysis,Springer. 117-123 (1997)
• [文献書誌] T.Kobayashi: "Invariant measures on homogeneous manifolds of reductive type" J.reine und angew.Math.490. 37-53 (1997)
• [文献書誌] K.Kurata: "A unique continuation theorem for the Schrodinger equation with singular magnetic field" Proc.A.M.S.125. 853-860 (1997)
• [文献書誌] A.Miyachi: "Atomic decomposition for Sobolev spaces and for the C^a_p spaces on general domains" Tsukuba J.Math.21. 59-96 (1997)
• [文献書誌] S.Moritoh: "Wavelet transforms and operators in various function spaces" New Trends in Microlocal Analysis. 59-68 (1997)
• [文献書誌] T.Oaku: "Algorithms for b-functions,reductions,and algebraic local cohomology groups of D-modules" Advances in Appl.Math.19. 61-105 (1997)
• [文献書誌] S.Omata, T.Okamura and K.Nakane: "Numerical analysis for the discrete Morse semiflow related to the Ginzburg Landau functional" to appear in Nonlinear World.
• [文献書誌] T.Suzuki and N.Mizoguchi: "Equations of gas combustion:S-shaped bifurcation and mushrooms" J.Differential Equations. 134. 183-215 (1997)
• [文献書誌] H.Tahara and R.Gerard: "Formal power series solutions of nonlinear first order partial differential equations" to appear in Funkcialaj Ekvacioj.
• [文献書誌] K.Taira: "Feller semigroups and Maarkov processes" Computational and Applied Mathematics. 16. 53-96 (1997)
• [文献書誌] S.Tajima: "Direct image of the de Rham system associated with a rational double point" Differential Geometry and Mathematical Physics. 39. 155-160 (1997)
• [文献書誌] K.Takasaki: "Dual isomonodromic problems and Whitham equations" to appear in Lett.Math.Phys.
• [文献書誌] Y.Takei and T.Kawai: "WKB analysis of Painleve transcendents with a large parameter.III---Local reduction of 2-parameter Painleve transcendents" to appear in Adv.in Math.
• [文献書誌] K.Takeuchi: "Edge-of-the-Wedge type theorems for hyperfunction solutions" Duke Math.J.89・1. 109-132 (1997)
• [文献書誌] Y.Tsutsumi, J.Ginibre and G.Velo: "On the Cauchy problem for the Zakharov system" to appear in J.Funct.Anal.
• [文献書誌] H.Watanabe: "The initial-boundary value problems for the heat operator in non-cylindrical domains" J.Math.Soc.Japan. 49・3. 399-430 (1997)
• [文献書誌] S.Takahashi, Y.Takahashi, O.Hatori and K.Tanahashi: "Commutative Banach algebras and BSE-norm" Math.Japonica.46(2). 273-277 (1997)
• [文献書誌] Y.Takahashi and M.Kato: "On the von Neumann-Jordan constant for Banach apaces" Proc.Amer.Math.Soc.125(4). 1055-1062 (1997)
• [文献書誌] N.Tanaka and H.Oka: "Abstract quasilinear integrodifferential equations of hyperbolic type" Nonlinear Anal.29. 903-925 (1997)
• [文献書誌] K.Yanagi and H.W.Chen: "On the Cover's conjecture on capacity of Gaussian channel with feedback" IEICE Trans.Fundamentals.80-A(11). 2272-2275 (1997)
• [文献書誌] K.Yoneda: "An application of Walsh Fourier analysis to weakly stationary processes" Acta Math.Hungar.76(4). 303-335 (1997)
• [文献書誌] H.Arai: "Morrey apaces and applications to hypoelliptic equations on Cauchy-Riemann manifolds" to appear in Proc.intern.Conf.on Aspects of Math.
• [文献書誌] S.Hasegawa and R.Sato: "On a d-parameter ergodic theorem for continuous semigroups of operators satifying norm conditions" Comment.Math.Univ.Carolinae. 38. 433-462 (1997)
• [文献書誌] S.Igari: "The Kakeya maximal operator with a special base" Approx.Theory and Appl.13. 1-7 (1997)
• [文献書誌] Y.Kanjin: "Hardy's inequalities for Hermite and Laguerre expansions" Bill.London Math.Soc.29. 331-337 (1997)
• [文献書誌] H.Kita: "On Hardy-Littlewood maximal functions in Orlicz spaces" Math.Nach.183. 135-155 (1997)
• [文献書誌] A.Miyachi: "Atomic decomposition for Sobolev spaces and for the C^a_p spaces on general domains" Tukuba Journal of Mathematics. 21(1). 59-96 (1997)
• [文献書誌] I.Miyamoto and Y.Okuyama: "On the double Norlund Summability of double Fourier series" Tamkang J.Math.22(2). 133-144 (1997)
• [文献書誌] H.Mizumachi and H.Sato: "Absolute continuity of similar translations" Journal of Kyoto University. 37. 317-326 (1997)
• [文献書誌] E.Nakai and K.Yabuta: "Pointwise multipliers for functions of weighted bounded mean oscillation on spaces of homogeneous type" Mathematica Japonica. 46. 15-28 (1997)
• [文献書誌] T.Nishishiraho: "Korovkin sets and mean ergodic theorems" to appear in I.Convex.Anal.
• [文献書誌] N.Ogata: "On the absolute convergence of lacunary Fourier series" to appear in Mathematica Japonica.48. (1998)
• [文献書誌] 大矢 雅則 編: "第36回実函数論・函数解析学合同シンポジウム講演集録" 147 (1998)
• [文献書誌] 佐藤亮太郎 編: "実解析学シンポジウム 1997仙台" 214 (1997)
• [文献書誌] 剣持 信幸 編: "第23回 発展方程式研究会報告集" 95 (1997)
• [文献書誌] 井上 純治 編: "第6回関数空間セミナー報告集" (1998)
• [文献書誌] 竹中 茂夫 編: "1997年度表現論シンポジウム報告集" 153 (1997)
• [文献書誌] 辛崎 秀樹 編: "「作用素論・作用素環論」研究集会報告集" 51 (1997)
• [文献書誌] 辛崎 秀樹 編: "「関数環論」研究集会報告集" (1997)
• [文献書誌] R.S.Ingarden, A.Kossakowski and M.Ohya: "Information Dynamics and Open Systems" Kluwer Academic Publishers, 320 (1997)
• [文献書誌] 堀田良之: "環と体1 岩波講座 現代数学の基礎15" 岩波書店, (1997)
• [文献書誌] 新井朝雄: "ヒルベルト空間と量子力学" 共立出版, (1997)
• [文献書誌] 新井朝雄, 杉浦光夫 編: "物理学の諸公理の数学的扱い(担当部分,pp.57--70)" 日本評論社, (1997)
• [文献書誌] 新井朝雄, 荒木不二洋 編: "数理物理への誘い「ゲージ理論における正準交換関係の表現とアハラノフボ-ム効果」(担当部分,pp.165--190)" 遊星社, (1997)
• [文献書誌] 石村隆一: "層の超局所理論と微分方程式" 千葉大学数学セミナリーノートNo1, (1997)
• [文献書誌] 倉田和浩, 村田實: "偏微分方程式1" 岩波講座現代数学の基礎, (1997)
• [文献書誌] K.Taira: "Brownian motion and index formulas for the de Rham complex" Mathematical Research,WILEY-VCH Verlag, (1998)
• [文献書誌] S.Tajima: "Geometric Phases and Bloch Electrons" SPS-DOST Lecture Notes in Mathematics,vol5,63, (1997)