Research Monographs:

1. Spectral Representations for Schrödinger Operators with Long-Range Potentials, Lecture Notes in Mathematics 727, Springer, 1979.



2. (with I. Knowles) Differential Equations and Mathematical Physics, Lecture Notes in Mathematics 1285, Springer, 1987.

Research Publications:

1. On the diagonalization of the measure matrix in the eigenfunction expansion for ordinary differential equations of the second order, Publ. RIMS, Kyoto Univ 1 (1966), 149 - 162.



2. Some remarks on the orthogonality of generalized eigenfunctions for singular second-order differential equations. Publ. RIMS, Kyoto Univ 2 (1966), 255 - 267.



3. Eigenfunction expansions associated with second-order differential equations for Hilbert space-valued functions, Publ. RIMS, Kyoto Univ 7 (1971), 1 - 55.



4. The principle of limiting absorption for second-order differential equations with operator-valued coefficients, Publ. RIMS, Kyoto Univ., 7 (1972), 518-619.



5. (with T. Ikebe). Limiting absorption method and absolute continuity for the Schrödinger operator, J. Math. Kyoto Univ., 12 (1972), 513-612.



6. Spectral and scattering theory for second-order differential operators with operator- valued coefficients, Osaka J. Math. 9(1972), 463 - 498.



7. The principle of limiting absorption for the non-selfadjoint Schrödinger in R^N (N not equal to 2), Publ. RIMS, Kyoto Univ 9 (1974), 397 - 428.



8. The principle of limiting absorption for the non-selfadjoint Schrödinger operator in R^2, Osaka J. Math. 11 (1974),295 - 306 .



9. Spectral theory for second-order differential operators with long-range operator- valued coefficients, I, Japan J. Math., New Ser. 1(1975), 311 - 349.



10. Spectral theory for second-order differential operators with long-range operator- valued coefficients, II, Japan J. Math., New Ser. 1(1975), 351 - 385.



11. Eigenfunction expansions for differential operators with long-range coefficients and their applications to the Schrödinger operators with long-range potentials, International Symposium on Mathematical problems in Theoretical Physics. Lecture Notes in Physics, Springer 39 (1975 ), 476 - 482 .



12. Eigenfunction expansions for Schrödinger operators , Sugaku 28 (1976), 311 - 322 (in Japaneese).



13. On the asymptotic behavior of the solution of the Schrödinger equation (-\DELTA + Q(y) - k^2)V = F, Osaka J. Math 14 (1977), 11 - 35.



14. Eignefunctions expansions for the Schrödinger operators with long-range potentials Q(y) = O(|y|^(-\epsilon), \epsilon > 0,, Osaka J. Math 14 (1977), 37 - 52.



15. On the S-matrix for Schrödinger operators with long-range potentials, J. Reine Angew. Math. 324 (1980),99 - 116.



16. Some properties of the scattering amplitude and the inverse scattering problem, Preprint Series 103, Sonderforshungsbereich 123, University of Heideberg (1980).



17. Some properties of the scattering amplitude and the inverse scattering problem, Osaka J. Math 19(1982), 527 - 547.



18. An inverse problem in potential theory and the inverse scattering problem, J. Math. Kyoto Univ. 22 (1982), 315 - 329 .



19. Extended limiting absorption method and analyticity of S-matrix, J. Reine Angew. Math. 243 (1983), 1 - 22.



20. An asymptotic behavior of S-matrix and the inverse scattering problem, J. Math. Phys., 25 (1984), 3105-3111.



21. An approximation formula in the inverse scattering problem, J. Math. Phys. 27(1986), 1145 - 1153.



22. An asymptotic formula and approximation formula in the inverse scattering problem, Lecture Notes of Mathematics 1218, Springer (1986), 190 - 200.



23. Schrödinger operators with a nonspherical radiation condition, Pacific J. Math 126 (1987), 331-359.



24. Inverse scattering for the plasma wave equation starting with large-t data, J. Phys. A. Math.Gen.,21 (1988),1623 - 1631 .



25. A remark on the limiting absorption principle for the reduced wave equation with two unbounded media, Pacific J. Math., 136 (1989), 183-208.
26. (with W. D.  Evans and R. T.  Lewis) Finiteness of bound states of general N-body operators, Proceedings of the 7th Czechoslovac Conference on Differential Equations and Their Applications. Held in Prague, 1989. Tuebner Text zur Mathematik Band 118, Teubner Verlag (1990), 159 - 162.



27. (with W. D.  Evans and R. T.  Lewis) Eigenvalue properties of non-isotropic Schrödinger operators with applications , Ordinary and partial differential equations Volume III, Proceedings of the Eleventh Dundee Conference, 1990, Longman Scientific & Technical (1991), 80 - 94.



28. (with W. D.  Evans and R. T.  Lewis).   Some geometric spectral properties of N-body Schrödinger operators,  Arch. Rational Mech. Anal., 113 (1991), 370-400. DVI



29. (with W. D.  Evans and R. T.  Lewis) Agmon's spectral function for Fermion particles, Preprint Series 643, Sonderforshungsbereich 123, University of Heideberg (1991).



30. (with W. D.  Evans and R. T.  Lewis) Geometric spectral properties of N-body Schrödinger operators, Part II, Phil. Transactions of the Royal Society of London A, 338 (1992), 113-144. DVI



31. (with W. D.  Evans and R. T.  Lewis) Zhislin's Theorem Revisited, J. Analyse Math 58 (1992), 191-212. DVI



32. (with W. D.  Evans and R. T.  Lewis) The Agmon spectral function for molecular Hamiltonian with symmetry restrictions, Phil.Trans. Royal Society of London A, 440 (1993), 621-638. DVI



33. (with W. D.  Evans and R. T.  Lewis) Eigenvalue properties of Schrödinger operators, Advanced Studies in Pure Mathematics, Spectral and Scattering Theory and Applications, Kinokuniya and Academic Press 23(1994), 27 - 55.



34. (with C. Pladdy and T. Umeda) Asymptotic behavior of the resolvent of the Dirac operator , Operator Theory: Advances and Applications, Birkhäuser 70 (1993), 45 - 54.



35. (with W. Jäger) The Limiting absorption principle for the reduced wave operator with cylindrical discontinuity, Preprint Series. IWR (SFB359) 94-74, University of Heidelberg, 1994. DVI



36. Radiation condition method in spectral and scattering theory, Recent developmets in evolution equations, Pitmans Research Notes in Mathematics Series 324 (1995),18 - 31.
    
37. The reduced wave operator with two unbounded media, Operator Theory: Advances and Applications, Birkhäuser 78 (1995), 291 - 297.
    
38. (with C. Pladdy and T. Umeda) Resolvent estimates for Dirac operators, Analysis 15 (1995), 123-149. DVI
    
39. (with W. Jäger) On the spectrum of the reduced wave operator with cylindrical discontinuity, Forum Mathematicum, 9 (1997), 29-60. DVI
    
40. (with W. Jäger)The reduced wave equation in layered materials, Osaka J. Math., 34 (1995), 267-301. DVI
    
41. (with C. Pladdy and T. Umeda) Radiation condition for Dirac operators, Kyoto J. Math. 37(1998), 567 - 584. DVI
    
42. (with W. Jäger) The uniqueness of the solution of the Schrödinger equation with discontinuous coefficients (1996), Reviews of Mathematical Physics. 10 (1998), 963 - 987. DVI
43. The limiting equation of the Neumann Laplacians on shrinking domains, Electronic J. Differential Equations 2000/31, 1-25.
    DVI
44. (with W. D.  Evans) Neumann Laplacian on domains and operators on associated trees, Quart. J. Math. Oxford  51 (2000), 313-34. DVI
45. Convergence of the Neumann Laplacians on shinking domains, Analysis 21 (2001), 171-204. DVI
46. (with C. Bennewitz) An embedding norm and the Lindqvist trigonometric functions, Electronic J. Differential Equations 2002/86, 1-6. DVI