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Atsushi INOUE

Professor, Department of Mathematics,
Tokyo Institute of Technology
Fields of interest: PDE(linear, non-linear), Mathematical Physics, Random MatrixTheory, Super-analysis, Functional Derivative Equations

TelF (03)5734-2205
FaxF (03)5734-2738
E-mailF inoue@math.titech.ac.jp

2008 Lectures ``Analysis on superspace"

Lectures on Analysis on superspace - live

ATLOM's book in preparation

Introduction to SuperAnalysis and its Application: on 06-12.14

Preprints

  1. A.Inoue, {Examples of $2\times2$-system version of Egorov's theorem}, pdf-file.
  2. A.Inoue, {An extension of the method of characteristic to a system of Partial Differential Operators -- an application to the Weyl equation with external field by ``Super Hamiltonian path-integral method"}, pdf-file.

Recent Published Papers (1991~)

  1. A.Inoue and Y. Maeda, {Foundations of calculus on super Euclidean space ${\mathfrak R}^{m|n}$ based on a Fr\'echet-Grassmann algebra}, Kodai Math.J., 14 (1991), 72--112,
  2. A.Inoue, { Foundation of real analysis on the superspace ${\mathfrak R}^{m|n}$ over the $\infty$-dimensional Fr\'echet-Grassmann algebra}, J.Fac.Sci.Univ.Tokyo, 39 (1992), 419--474,
  3. A.Inoue, {A tiny step towards functional derivative equations ---a strong solution of the space-time Hopf equation}, in ``The Navier-Stokes equations II--Theory and Numerical Methods'' (ed. Heywood et al), Springer Lec.Notes Math. 1530 (1992), 246--261,
  4. A.Inoue, {A remark on functional derivative equations}, in `` Geometry and its application'' (ed. T. Nagano et al.) World Scientific Publ. (1993), 39--49,
  5. A.Inoue, {A new construction of a fundamental solution for the free Weyl equation ---An example of superanalysis}, in ``Nonlinear Waves" (eds. R. Agemi, Y. Giga and T. Ozawa), Gakuto International Series, Mathematical Sciences and Applications, 10 (1997), 169--182,
  6. A.Inoue, {The first term of spectral asymptotic formula related to the continuum mechanics --generalizations of Weyl's theorem}, in ``Navier-Stokes equations: theory and numerical methods" ied. R. Salvi), Longman, (1998), 184--192,
  7. A.Inoue, {On a construction of the fundamental solution for the free Weyl equation by Hamiltonian path-integral method ---an exactly solvable case with ``odd variable coefficients"}, T\^ohoku J.Math.,50 (1998), 91--118,
  8. A.Inoue, {On a construction of the fundamental solution for the free Dirac equation by Hamiltonian path-integral method ---the classical counterpart of Zitterbewegung}, Japanese J.Math.,24 (1998), 297--334,
  9. A.Inoue, { On a ``Hamiltonian path-integral" derivation of the Schr\"odinger equation}, Osaka J.Math.,36 (1999), 111--150,
  10. A.Inoue, { A partial solution for Feynman's problem -- a new derivation of the Weyl equation}, in ``Mathematical Physics and Quantum Field Theory", Electron. J. Diff.Eqns., Conf.04, 2000, pp. 121-145. ps-file, pdf-file.
  11. A.Inoue and Y. Nomura, {Some refinements of Wigner's semi-circle law for Gaussian Random Matrices using superanalysis}, Asymptotic Analysis, 23 (2000), 329--375. ps-file, pdf-file.
  12. A.Inoue and Y. Maeda, {On a construction of a good parametrix for the Pauli equation by Hamiltonian path-integral method --- an application of superanalysis}, {Japanese J. Math.{29}(2003) 27-107}. ps-file, pdf-file.

Published papers selected (1970`1990)

  1. A. Inoue, {On the mixed problem for the wave equation with an oblique boundary condition}, J. Fac. Sci. Univ. Tokyo, 16 (1970), 313--329.
  2. A. Inoue, {Sur $ \square u + u^3 = f $ dans un domaine non cylindrique}, J.Math.Anal.Appl., 46 (1973), 777--819.
  3. A. Inoue, {On a mixed problem for $ \square $ with discontinuous boundary condition (I)}, J.Fac.Sci.Univ.of Tokyo., 21 (1974), 85--72.
  4. A. Inoue, {On a mixed problem for d'Alembertian with a mixed boundary condition -an example of moving boundary}, Publ.RIMS. Kyoto Univ., 11 (1976), 339--401.
  5. A. Inoue and M. Wakimoto, {On existence of solutions of the Navier-Stokes equation in a time dependent domain}, J.Fac.Sc.Univ.of Tokyo, 24 (1977), 303--320.
  6. A. Inoue, {On a mixed problem for $\square$ with a discontinuous boundary condition (II) --an example of moving boundary}, J.Math.Soc.Japan, 30 (1978), 633--651.
  7. A. Inoue and T. Funaki, {On a new derivation of the Navier-Stokes equation}, Commun.Math.Phys., 65 (1979), 83--90.
  8. A. Inoue, {On Yamabe's problem -by a modified direct method-}, 34 (1982), 499--507.
  9. A. Inoue and Y. Maeda, {On integral transformations associated with a certain Lagrangian -- as a prototype of quantization}, J.Math. Soc.Japan, 37 (1985), 219--244.
  10. A. Inoue, {Some examples exhibiting the procedures of renormalization and gauge fixing -- Schwinger-Dyson equations of first order}, Kodai Math.J. 9 (1986), 134--160.
  11. A. Inoue, {Strong and classical solutions of the Hopf equation ---an example of Functional Derivative Equation of second order}, T\^ ohoku Math.J. 39 (1987), 115--144.
  12. A. Inoue, {On Hopf type functional derivative equations for $\square u + cu + b u^2 +a u^3 = g$ on $\Omega\times{\bold R}_+$.I. The existence of solutions}, J.Math.Anal.Appl. 152 (1990), 61--87.
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e-mail : inoue@math.titech.ac.jp
Place: 314B, 3F, Main Building of Oh-okayama campus
tel(office): 03-5734-2203(direct)[rarely exist]
tel(dept): 03-5734-2205(direct)[exist near here]
Department of Mathematics, Tokyo Institute of Technology
PO:152-8551, 2-12-1 Oh-okayama, Meguro-ku, Tokyo