Papers on Continuous Spectral Problems and Their Applications


  1. Lars-Erik Andersson: Inverse eigenvalue problems for a Sturm-Liouville equation in impedance form. Inverse Problems 4 (1988), 929-971.

  2. F. V. Atkinson: Asymptotics of an eigenvalue problem involving an interior singularity. Argonne National Laboratory Proc. ANL-87-26 (1988), vol. 2, 1-18.

  3. F. V. Atkinson: Asymptotics of eigenfunctions for some nonlinear elliptic problems. Differential Equations and Applications, Vol. I, II (Columbus, OH, 1988), 26-49, Ohio Univ. Press, Athens, OH, 1989.

  4. F. V. Atkinson: Higher approximations to eigenvalues for a nonlinear elliptic problem. Nonlinear Diffusion Equations and Their Equilibrium States, 3 (Gregynog, 1989), 39-69. Progr. Nonlinear Differential Equations Appl. 7, Birkhauser Boston, Boston, MA, 1992.

  5. F. V. Atkinson & C. T. Fulton: Some limit circle eigenvalue problems and asymptotic formulae for eigenvalues. Ordinary and Partial Differential Equations (Dundee, 1982), 28-55. Lecture Notes in Math. 964, Springer, Berlin, 1982.

  6. F. V. Atkinson & C. T. Fulton: Asymptotic formulae for eigenvalues of limit circle problems on a half line. Ann. Mat. Pura Appl. (4) 135 (1983-84), 363-398.

  7. F. V. Atkinson & C. T. Fulton: Asymptotics of Sturm-Liouville eigenvalues for problems on a finite interval with one limit-circle singularity. I. Proc. Roy. Soc. Edinburgh A99 (1984), 51-70.

  8. F. V. Atkinson & A. B. Mingarelli: Asymptotics of the number of zeros and of the eigenvalues of general weighted Sturm-Liouville problems. J. Reine Angew. Math. 375/376 (1987), 380-393.

    BBB

  9. Paul B. Bailey, Burton S. Garbow, Hans G. Kaper & Anton Zettl: Eigenvalue and eigenfunction computations for Sturm-Liouville problems. ACM Trans. Math. Software 17 (1991), 491-499.
  10. Paul B. Bailey, Burton S. Garbow, Hans G. Kaper & Anton Zettl: Algorithm 700: A FORTRAN software package for Sturm-Liouville problems. ACM Trans. Math. Software 17 (1991), 500-501.
  11. Paul B. Bailey, Williams N. Everitt & Anton Zettl: Algorithm 810: The SLEIGN2 Sturm-Liouville Code. ACM Trans. Math. Software 27 (2001), 143-192.
  12. Elgiz Bairamov & Allan M. Krall: Dissipative operators generated by the Sturm-Liouville differential expression in the Weyl limit circle case. J. Math. Anal. Appl. 254 (2001), 178-190.
  13. A. Batkai, P. Binding, A. Dijksma, R. Hryniv & H. Langer: Spectral problems for operator matrices. Math. Nachr. 278 (2005), 1408-1429.
  14. P. Binding & P. Browne: Application of two parameter eigencurves to Sturm-Liouville problems with eigenparameter-dependent boundary conditions. Proc. Roy. Soc. Edinburgh A125 (1995), 1205-1218.
  15. P. Binding & P. Browne: Oscillation theory for indefinite Sturm-Liouville problems with eigenparameter-dependent boundary conditions. Proc. Roy. Soc. Edinburgh A127 (1997), 1123-1136.
  16. P. Binding & P. Browne: Left definite Sturm-Liouville problems with eigenparameter dependent boundary conditions. Differential Integral Equations 12 (1999), 167-182.
  17. P. Binding & P. Browne: Sturm-Liouville problems with non-separated eigenvalue dependent boundary conditions. Proc. Roy. Soc. Edinburgh A130 (2000), 239-247.
  18. P. Binding, P. Browne & K. Seddighi: Sturm-Liouville problems with eigenparameter dependent boundary conditions. Proc. Edinburgh Math. Soc. (2) 37 (1994), 57-72.
  19. P. Binding, P. Browne & B. Watson: Spectral problems for non-linear Sturm-Liouville equations with eigenparameter dependent boundary conditions. Canad. J. Math. 52 (2000), 248-264.
  20. P. Binding, P. Browne & B. Watson: Inverse spectral problems for Sturm-Liouville equations with eigenparameter dependent boundary conditions. J. London Math. Soc. (2) 62 (2000), 161-182.
  21. P. Binding, P. Browne & B. Watson: Sturm-Liouville problems with boundary conditions rationally dependent on the eigenparameter. I. Proc. Edinb. Math. Soc. 45 (2002), 631-645.
  22. P. Binding, P. Browne & B. Watson: Sturm-Liouville problems with boundary conditions rationally dependent on the eigenparameter. II. J. Comput. Appl. Math. 148 (2002), 147-168.
  23. P. Binding, R. Hryniv, H. Langer & B. Najman: Elliptic eigenvalue problems with eigenparameter dependent boundary conditions. J. Differential Equations 174 (2001), 30-54.
  24. P. A. Binding & H. Volkmer: Existence and asymptotics of eigenvalues of indefinite systems of Sturm-Liouville and Dirac type. J. Differential Equations 172 (2001), 116-133.
  25. P. A. Binding & H. Volkmer: Interlacing and oscillation for Sturm-Liouville problems with separated and coupled boundary conditions. J. Comput. Appl. Math. 194 (2006), 75-93.
  26. P. A. Binding & H. Volkmer: Inverse oscillation theory for Sturm-Liouville problems with non-separated boundary conditions. Inverse Problems 23 (2007), 343-355.
  27. M. S. Birman & M. Z. Solomjak: The principal term of the spectral asymptotics for "non-smooth" elliptic problems. Functional Anal. Appl. 4 (1970), 265-275.
  28. A. Boumenir: A comparison theorem for self-adjoint operators. Proc. American Math. Soc. 111 (1991), 161-175.
  29. A. Boumenir: Irregular sampling and the inverse spectral problem. J. Fourier Anal. Appl. 5 (1999), 377-387.
  30. A. Boumenir: A rigorous verification of a numerically computed eigenvalue. Comput. Math. Appl. 38 (1999), 39-41.
  31. A. Boumenir: Sampling for the fourth-order Sturm-Liouville differential operator. J. Math. Anal. Appl. 278 (2003), 542-550.
  32. A. Boumenir: The reconstruction of an analytic string from two spectra. Inverse Problems 20 (2004), 833-846.
  33. A. Boumenir: An inverse spectral problem for the Laplacian. Appl. Anal. 84 (2005), 221-228.

    CCC

  34. Robert Carlson: Inverse spectral theory for some singular Sturm-Liouville problems. J. Differential Equations 106 (1993), 121-140.

  35. Robert Carlson: Large eigenvalues and trace formulas for matrix Sturm-Liouville problems. SIAM J. Math. Anal. 30 (1999), 949-962.

  36. Robert Carlson: Inverse eigenvalue problems on directed graphs. Trans. American Math. Soc. 351 (1999), 4069-4088.

  37. Robert Carlson: Eigenvalue estimates and trace formulas for the matrix Hill's equation. J. Differential Equations 167 (2000), 211-244.

  38. Haskiz Coskun & B. J. Harris: Estimates for the periodic and semi-periodic eigenvalues of Hill's equation. Proc. Roy. Soc. Edinburgh A130 (2000), 991-998.

    DDD

  39. A. Dijksma: Eigenfunction expansions for a class of J-selfadjoint ordinary differential operators with boundary conditions containing the eigenvalue parameter. Proc. Roy. Soc. Edinburgh A86 (1980), 1-27.

  40. Ondrej Dosly: Oscillation criteria and the discreteness of the spectrum of selfadjoint, even order, differential operators. Proc. Roy. Soc. Edinburgh A119 (1991), 219-232.

    EEE

  41. A. E. Etkin: On an abstract boundary value problem with the eigenvalue parameter in the boundary condition. Fields Inst. Commun. 25 (2000), 257-266.

    HHH

  42. V. Hardt, A. Konstantinov & R. Mennicken: On the spectrum of the product of closed operators. Math. Nachr. 215 (2000), 91-102.

  43. V. Hardt & R. Mennicken: On the spectrum of unbounded off-diagonal 2 times 2 operator matrices in Banach spaces. "Recent Advances in Operator Theory (Groningen, 1998)", 243-266. Oper. Theory Adv. Appl. 124. Birkhauser, Basel, 2001.

  44. M. Dauge & B. Helffer: Eigenvalues variation. I. Neumann problem for Sturm-Liouville operators. J. Differential Equations 104 (1993), 243-262.

  45. M. Dauge & B. Helffer: Eigenvalues variation. II. Multidimensional problems. J. Differential Equations 104 (1993), 263-297.

    FFF

  46. C. Fefferman & D. H. Phong: On the asymptotic eigenvalue distribution of a pseudodifferential operator. Proc. Nat. Acad. Sci. U.S.A. 77 (1980), 5622-5625.
  47. George Fix: Asymptotic eigenvalues of Sturm-Liouville systems. J. Math. Anal. Appl. 19 (1967), 519-525.
  48. Jacqueline Fleckinger & Michel L. Lapidus: Schrodinger operators with indefinite weight functions: asymptotics of eigenvalues with remainder estimates. Differential Integral Equations 7 (1994), 1389-1418.
  49. G. Freiling, T. Mazur & V. A. Yurko: A numerical algorithm for solving inverse problems for singular Sturm-Liouville operators. Adv. Dyn. Syst. Appl. 2 (2007), 95-105.
  50. Charles T. Fulton: Two-point boundary value problems with eigenvalue parameter contained in the boundary conditions. Proc. Roy. Soc. Edinburgh A77 (1977), 293-308.
  51. C. Fulton: Singular eigenvalue problems with eigenvalue parameter contained in the boundary conditions. Proc. Roy. Soc. Edinburgh A87 (1980/81), 1-34.
  52. Charles T. Fulton: An integral equation iterative scheme for asymptotic expansions of spectral quantities of regular Sturm-Liouville problems. J. Integral Equations 4 (1982), 163-172.
  53. Charles T. Fulton: On generating theorems and conjectures in spectral theory with computer assistance. Spectral Theory and Computational Methods of Sturm-Liouville Problems (Knoxville, TN, 1996), 285-299. Lecture Notes in Pure and Appl. Math. 191, Dekker, New York, 1997.
  54. Charles Fulton, David Pearson & Steven Pruess: Computing the spectral function for singular Sturm-Liouville problems. J. Comput. Appl. Math. 176 (2005), 131-162.
  55. Charles T. Fulton & Steven A. Pruess: Eigenvalue and eigenfunction asymptotics for regular Sturm-Liouville problems. J. Math. Anal. Appl. 188 (1994), 297-340.
  56. Charles T. Fulton & Steven A. Pruess: Erratum: "Eigenvalue and eigenfunction asymptotics for regular Sturm-Liouville problems" [J. Math. Anal. Appl. 188 (1994), 297-340]. J. Math. Anal. Appl. 189 (1995), 313-314.

    HHH

  57. B. J. Harris: A note on a paper of Atkinson concerning the asymptotics of an eigenvalue problem with interior singularity. Proc. Roy. Soc. Edinburgh A110 (1988), 63-71.
  58. B. J. Harris: Asymptotics of eigenvalues for regular Sturm-Liouville problems. J. Math. Anal. Appl. 183 (1994), 25-36.
  59. B. J. Harris & F. Marzano: Eigenvalue approximations for linear periodic differential equations with a singularity. Electron. J. Qual. Theory Differ. Equ. 1999, No. 7, 1-18.
  60. B. J. Harris & D. Race: Asymptotics of eigenvalues for Sturm-Liouville problems with an interior singularity. J. Differential Equations 116 (1995), 88-118.
  61. B. J. Harris & S. T. Talarico: On the eigenvalues of second-order linear differential equations with fractional transition points. Math. Proc. R. Ir. Acad. 99A (1999), 29-38.
  62. Harry Hochstadt: Asymptotic estimates for the Sturm-Liouville spectrum. Comm. Pure Appl. Math. 14 (1961), 749-764.
  63. Harry Hochstadt: A special Hill's equation with discontinuous coefficients. Amer. Math. Monthly 70 (1963), 18-26.
  64. Harry Hochstadt: Estimates of the stability intervals for Hill's equation. Proc. Amer. Math. Soc. 14 (1963), 930-932.
  65. A. Nematy Hoseanabady & A. Jodayree Akbarfam: Asymptotics eigenvalues for Sturm-Liouville problems. Proceedings of the 27th Annual Iranian Mathematics Conference (Shiraz, 1996), 223-232, Shiraz Univ., Shiraz, 1996.

    KKK

  66. Yutaka Kamimura: On the spectrum of an ordinary differential operator with an r-integrable complex-valued potential. J. London Math. Soc. (2) 20 (1979), 86-100.

  67. Yutaka Kamimura: A criterion for the complete continuity of the resolvent of a 2n-th order differential operator with complex coefficients. Proc. Roy. Soc. Edinburgh A116 (1990), 161-176.

  68. A. Kiselev: Imbedded singular continuous spectrum for Schro"dinger operators. J. American Math. Soc. 18 (2005), 571-603.

    LLL

  69. Nebojsa Lazetic: Estimates of eigen- and associated functions of the Sturm-Liouville operator with discontinuous coefficients. (Russian) Dokl. Akad. Nauk SSSR 258 (1981), 541-544.

    MMM

  70. Hiroyuki Matsumoto: Semiclassical asymptotics of eigenvalues for Schrodinger operators with magnetic fields. J. Funct. Anal. 129 (1995), 168-190.
  71. A. McNabb, R. S. Anderssen & E. R. Lapwood: Asymptotic behavior of the eigenvalues of a Sturm-Liouville system with discontinuous coefficients. J. Math. Anal. Appl. 54 (1976), 741-751.

    NNN

  72. S. A. Nazarov: New series of asymptotics of eigenvalues of the Sturm-Liouville problem with rapidly oscillating coefficients. Math. Notes 52 (1992), 1134-1136.
  73. S. A. Nazarov & O. R. Polyakova: Asymptotics of eigenvalues of the Neumann problem in a domain with a narrow connector. Siberian Math. J. 33 (1992), 618-633.

    PPP

  74. Steven Pruess, Charles T. Fulton & Yuantao Xie: An asymptotic numerical method for a class of singular Sturm-Liouville problems. SIAM J. Numer. Anal. 32 (1995), 1658-1676.

    RRR

  75. David Race: The theory of J-selfadjoint extensions of J-symmetric operators. J. Differential Equations 57 (1985), 258-274.

  76. Susumu Roppongi: Asymptotics of eigenvalues of the Laplacian with small spherical Robin boundary. Osaka J. Math. 30 (1993), 783-811.

  77. G. V. Rozenbljum: Distribution of the discrete spectrum of singular differential operators. Soviet Math. Dokl. 13 (1972), 245-249.

  78. E. M. Russakovskii: An operator treatment of a boundary value problem with a spectral parameter that occurs polynomially in the boundary conditions. (Russian) Funkcional. Anal. i Prilozen. 9 (1975), no. 4, 91-92.

  79. E. M. Russakovskii: Operator treatment of a boundary value problem with a spectral parameter that occurs rationally in the boundary conditions. (Russian) Teor. Funktsii Funktsional. Anal. i Prilozhen. 30 (1978), 120-128, v.

  80. E. M. Russakovskii: Operator treatment of a boundary value problem with a spectral parameter that occurs rationally in the boundary conditions. II. (Russian) Teor. Funktsii Funktsional. Anal. i Prilozhen. 31 (1979), 140-145, 169.

    SSS

  81. A. M. Savchuk & A. A. Shkalikov: Sturm-Liouville operators with distribution potentials. Trans. Moscow Math. Soc. 2003, 143-192.

  82. A. M. Savchuk & A. A. Shkalikov: Inverse problem for Sturm-Liouville operators with distribution potentials: reconstruction from two spectra. Russ. J. Math. Phys. 12 (2005), 507-514.

  83. A. A. Shkalikov: Boundary value problems for ordinary differential equations with a parameter in the boundary conditions. J. Soviet Math 33 (1986), 1311-1342.

  84. Naohiro Suzuki: Semiclassical asymptotics of eigenvalues for Dirac operators with magnetic fields. J. Math. Anal. Appl. 253 (2001), 406-413.

    TTT

  85. Hideo Tamura: The asymptotic eigenvalue distribution for non-smooth elliptic operators. Proc. Japan Acad. 50 (1974), 19-22.

    VVV

  86. V. A. Vinokurov & V. A. Sadovnichi: Asymptotics of eigenvalues and eigenfunctions and a trace formula for a potential with delta-functions. Differ. Equ. 38 (2002), 772-789.

    WWW

  87. J. Walter: Regular eigenvalue problems with eigenvalue parameter in the boundary condition. Math. Z. 133 (1973), 301-312.

    YYY

  88. Vjacheslav A. Yurko: The inverse spectral problem for differential operators with nonseparated boundary conditions. J. Math. Anal. Appl. 250 (2000), 266-289.

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