List of publications (M. Demuth)

Prof. Dr. Michael Demuth
Institute of Mathematics
TU Clausthal

Books:

  1. Determining Spectra in Quantum Theory
    (together with M. Krishna),
    Birkhäuser, Boston, 2005.
  2. Stochastic Spectral Theory for Selfadjoint Feller Operators,
    (together with J. van Casteren),
    Birkhäuser, Basel, 2000.

Articles:

  1. Estimating the number of eigenvalues of linear operators on Banach spaces,
    (together with F. Hanauska, M. Hansmann, G. Katriel)
    J. Funct. Anal., 268 (2015), 1032-1052.
  2. On the distribution of the discrete spectrum of nuclearly perturbed operators in Banach spaces,
    (together with F. Hanauska)
    Indian J. Pure Appl. Math., 46 (2015), no. 4, 441-462.
  3. Lieb-Thirring type inequalities for Schrödinger operators with a complex-valued potential,
    (together with M. Hansmann, G. Katriel)
    Integral Equations Operator Theory 75.1 (2013), 1-5.
  4. Eigenvalues of non-selfadjoint operators: a comparison of two approaches,
    (together with M. Hansmann, G. Katriel)
    Operator Theory, Advances and Applications, Vol 232 (2013), 107-163
  5. On the role of the comparison function in the spectral theory of selfadjoint operators,
    (together with M. Hansmann),
    Comm. Math. Analysis Conference 03 (2011), 1-11.
  6. On spectral stability for the fractional Laplacian perturbed by unbounded obstacles,
    (together with M. Hansmann),
    Math. Nachr. 282.9 (2009), 1265-1277.
  7. On the discrete spectrum of non-selfadjoint operators,
    (together with M. Hansmann, G. Katriel),
    J. Funct. Anal. 257 (2009), 2742-2759.
  8. On finiteness of the sum of negative eigenvalues of Schrödinger operators,
    (together with H.Katriel),
    Bull. Kerala Math. Assoc. Special Issue (2009), 87-104. Edited by S.R.S. Varadhan.
  9. Eigenvalue inequalities in terms of Schatten norm bounds on differences of semigroups, and application to Schrödinger operators,
    (together with H. Katriel),
    Ann. Henri Poincaré 9 (2008), 817 - 834.
  10. Spectral consequences due to general Hölder's inequalities and domination of semigroups,
    Operator Theory: Advances and Applications 187 (2008), 125 - 140.
  11. On the distribution of eigenvalues of non-selfadjoint operators,
    (together with M. Hansmann, G. Katriel),
    Preprint TU Clausthal, Mathematikbericht 2008/1, 2008.
  12. Hölder's inequality for perturbations of positive semigroups
    by potentials,
    (together with W. Arendt)
    J. Math. Anal. Appl. 316 (2006), 652-663.
  13. Resolvent differences for general obstacles,
    (together with J. Brasche),
    Progress in Nonlinear Differential Equations and Their Applications 64 (2005), 63 - 70.
  14. Dynkin's formula and large coupling convergence,
    (together with J. Brasche),
    Journal of Functional Analysis 219 (2005), 34-69.
  15. Stable continuous spectra for differential operators of arbitrary order,
    (together with M. Baro and E. Giere ),
    Analysis and Applications 3 (2005), 223-250.
  16. Equilibrium potentials in scattering theory,
    (together with A. Noll),
    Contemporary Mathematics 307 (2002), 95-106.
  17. Schrödinger operators with empty singularly continuous spectrum, (together with M. Baro),
    Preprint TU Clausthal, Mathematik-Berichte 2001/07, 2001.
  18. A semigroup criterion for the completeness of scattering systems, (together with E. Giere and K.B. Sinha),
    Operator Theory, Advances and Applications 126 (2001), 93-102.
  19. On perturbations for the continuous spectra of semigroup generators,
    Lecture Notes in Pure and Applied Mathematics 215 (2001), 347 - 354.
  20. Stochastic processes and the spectrum of Feller operators,
    Canadian Mathematical Society, Conference Proceedings 29 (2000), 135 - 142.
  21. Schrödinger operators with empty singularly continuous spectra, (together with K.B. Sinha).
    Math. Phys., Analysis and Geometry 2 (1999), 223 - 244.
  22. Traces and trace norms for semigroup differences,
    Operator Theory, Advances and Applications 108 (1999), 209 - 219.
  23. Capacitary estimates for the scattering phase,
    (together with I. McGillivray),
    J. Math. Anal. Appl. 237 (1999), 253 - 271.
  24. Integral conditions for the asymptotic completeness of two-space scattering systems,
    Helv. Phys. Acta. 71 (1998), 117 - 132.
  25. Completeness of scattering systems with obstacles of finite capacity, (together with J. van Casteren),
    Operator Theory, Advances and Applications 102 (1998), 38 - 50.
  26. Scattering for Schrödinger operators with magnetic fields,
    (together with E. Ouhabaz),
    Math. Nachrichten 185 (1997), 49 - 58.
  27. Capacity and spectral theory,
    (together with I. McGilligvray and A. Noll),
    Mathematical Topics 14, Advances in Partial Differential Equations, Akademie Verlag (1997), 12 - 77.
  28. Finite capacities in spectral theory,
    (together with F. Gesztesy, J. van Casteren, Z. Zhao),
    Operator Theory, Advances and Applications 78 (1995), 89 - 97.
  29. Trace norm estimates for products of integral operators and diffusion semmigroups,
    (together with P. Stollmann, G. Stolz and J. van Casteren),
    Integral Equations and Operator Theory 23 (1995), 145 - 153.
  30. Schrödinger semigroups - geometric estimates in terms of the occupation time, (together with W. Kirsch, I. McGillivray).
    Comm. Part. Diff. Equat. 20 (1995), 37 - 57.
  31. Non trace class operators with finite trace,
    (together with P. Stollmann and J. van Casteren),
    Seminar Notes in Functional Analysis, Lousiana State University, 1993-94, (1994), 119 - 128.
  32. A Hilbert-Schmidt property of resolvent differences of singularly perturbed generalized Schrödinger Operators,
    (together with J. van Casteren),
    Lecture Notes in Pure and Applied Mathematics 155 (1994), 117 - 144.
  33. Occupation time asymptotics with an application to the decay of eingenfunctions (together with W. Kirsch and I. McGillivray),
    Operator Theory, Advances and Applications 70 (1994), 133 - 135.
  34. Framework and results of stochastic spectral analysis,
    (together with J. van Casteren),
    Operator Theory, Advances and Applications 70 (1994), 123 - 132.
  35. Rate of convergence for large coupling and for semi-classical limits,
    (together with F. Jeske and W. Kirsch),
    Ann. Inst. H. Poincare, 59 (1993), 327 - 355.
  36. Perturbation of spectral measures for Feller operators,
    Operator Theory, Advances and Applications 57, (1992), 27 - 37.
  37. Perturbations of generalized Schrödinger operators in stochastic spectral analysis, (together with J. van Casteren),
    Lecture Notes in Physics 403 (1992), 1 - 15.
  38. Spectral properties of Schrödinger operators for large coupling and semi-classical asymptotics,
    "Functional Analysis and Related Topics",
    eds.: S. Koshi, World Sientific (1991), 72 - 84.
  39. On potential continuity in stochastic spectral analysis,
    (together with J. van Casteren),
    "Rigorous Results in Quantum Dynamics",
    eds.: J. Dittrich, P. Exner, World Scientific (1991), 270 - 274.
  40. On large coupling operator norm convergence of resolvent differences,
    Journal of Mathematical Physics 32 (1991), 1522 - 1530.
  41. On topics in spectral and stochastic analysis for Schrödinger operators, "Recent Developements in Quantum Mechanics",
    eds.: A. M. Boutet-de-Monvel et. al., Kluwer Academic Publisher (1990), 223 - 242.
  42. On generalized Schrödinger semigroups and Feynman-Kac-formula,
    (with J. van Casteren),
    "Schrödinger Operators, Standard and Non-Standard",
    eds.: P. Exner and P. Seba, World Scientific (1989), 321 - 331.
  43. On differences of heat semigroups,
    (together with J. van Casteren),
    Ann. Sci. Univ. Blaise Pascal 93 (1989), 119 - 147.
  44. On spectral theory for selfadjoint Feller generators,
    (with J. van Casteren),
    Reviews in Mathematical Physics 1 (1989), 325 - 414.
  45. On perturbations of selfadjoint Feller generators,
    Lecture Notes Physics 324 (1989), 40 - 54.
  46. On spectral properties for regular and singular generators of Schrödinger semigroups,
    Teubner Texte zur Mathematik 112 (1988), 52 - 62.
  47. Schrödinger Operatoren und Quantentheorie,
    (together with H. Baumgärtel),
    Mitteilungen der Mathematischen Gesellschaft, No. 1-2/88 (1988).
  48. Invariance of the essential spectra for perturbations with unbounded hard cores,
    (together with E. Brüning and F. Gesztesy),
    Lett. Math. Phys. 13 (1987), 69 - 77.
  49. On stochastic methods in spectral theory of Schrödinger operators,
    Czech.J.Phys. B 37 (1987), 1020 - 1027.
  50. Die Spektraltheorie von Schrödinger Operatoren als Teil der Mathematischen Physik,
    Ergebnisse der Schule Junger Mathematiker, KMU, Leipzig (1986),
    17 - 32.
  51. On scattering for Schrödinger operators with anisotropic and singular potentials,
    Math. Nachr. 129 (1986), 185 - 196.
  52. Zeitabhängige Streutheorie für Erzeuger von Markov-Prozessen mit anisotropen und singulären Potentialen,
    (monograph for the habilitation)
    Report Inst. Math., R-Math-04/85 (1985), 1 - 162.
  53. Asymptotic completeness in the singular potential scattering derived by geometric methods,
    Lett. Math. Phys. 10 (1985), 247 - 254.
  54. On transformations in the Feynman-Kac-Formula and quantum- mechanical N-body-systems,
    Math. Nachr. 122 (1985), 109 - 118.
  55. Necessary conditions for the existence of wave operators,
    (together with M. Wollenberg),
    Math. Nachr. 114 (193), 293 - 301.
  56. On necessary and sufficient conditions for the Cook-criterion,
    Math. Nachr. 113 (1983), 171 - 185.
  57. On resonances in mathematical scattering theory,
    Banach Center Publications, VIII (1982), 237 - 240.
  58. Scattering by potentials infinite on unbounded regions,
    Math. Nachr. 107 (1982), 315 - 325.
  59. On time-dependent scattering theory in Krein-spaces,
    Math. Nachr. 102 (1981), 107 - 125.
  60. On scattering of diffusion process generators,
    Math. Nachr. Phys. 4 (1980), 417 - 424.
  61. On diffusion processes and spectral theory,
    Proceedings of the Brasov International School 1979,
    "Recent Advances in Statistical Mechanics",
    Bukarest 1979, 647 - 655.
  62. Decoupling by a projection,
    (together with H. Baumgärtel),
    Reports on Math. Phys. 15 (1979), 173 - 186.
  63. On the equality of resonances (poles of the scattering amplitude) and virtual poles, (together with H. Baumgärtel and M. Wollenberg),
    Math. Nachr. 86 (1978),167 - 174.
  64. On unstable isolated and embedded eigenvalues,
    Math. Nachr. 77 (1977), 93 - 100.
  65. Nonanalytic perturbation of compact operators,
    Math. Nachr. 74 (1976), 313 - 320.
  66. Pole approximation and spectral concentration,
    Math. Nachr. 73 (1976), 65 - 72.
  67. Perturbation of unstable eigenvalues of finite multiplicity,
    (together with H. Baumgärtel),
    J. Functional Analysis 22 (1976), 187 - 203.
  68. On the perturbation of unstable isolated eingenvalues,
    Math. Nachr. 64 (1974), 345 - 356.
  69. Corrections to the Wannier-excition: Second order electron-hole
    interaction,
    Ann. Physik 30 (1973), 216 - 228.

Editorial Work:

Journals:
  1. Integral Equations and Operator Theory, Birkhäuser
Proceedings:
  1. Operator Calculus and Spectral Theory, Conference in Lambrecht,
    Birkhäuser, Series: Operator Theory, Vol. 57, 1992
    (Editor together with B. Gramsch and B.-W. Schulze).
  2. Mathematical Results in Quantum Mechanics, Conference in Blossin,
    Birkhäuser, Series: Operator Theory: Vol. 70, 1994
    (Editor together with P. Exner, H. Neidhardt and V. Zagrebnov).
  3. Partial Differential Operators and Mathematical Physics,
    Conference in Holzhau, Birkhäuser, Series: Operator Theory,
    Vol. 78, 1995 (Editor together with B.-W. Schulze).
  4. Differential Equations, Asymptotic Analysis and Mathematical Physics,
    Conference in Potsdam, Akademie Verlag, Series: Mathematical Research, Vol. 100, 1997 (Editor together with B.-W. Schulze).
  5. Partial Differential Equations and Spectral Theory, Conference in Clausthal,
    Birkhäuser, Series: Operator Theory, Vol. 126, 2001
    (Editor together with B.-W. Schulze).
Series: Advances in Partial Differential Equations
  1. Pseudo-Differential Calculus and Mathematical Physics.
    Advances in Partial Differential Equations 1.
    Akademie Verlag, Berlin, 1994.
    (Editor together with E. Schrohe and B.-W. Schulze)
  2. Boundary Value Problems, Schrödinger Operators, Deformation
    Quantization.
    Advances in Partial Differential Equations 2.
    Akademie Verlag, Berlin, 1995.
    (Editor together with E. Schrohe and B.-W. Schulze)
  3. Schrödinger Operators, Markov-Semigroups, Wavelet Analysis,
    Operator Algebras.
    Advances in Partial Differential Equations 3.
    Akademie Verlag, Berlin, 1996.
    (Editor together with E. Schrohe, B.-W. Schulze and J. Sjöstrand)
  4. Spectral Theory, Microlocal Analysis, Singular Manifolds.
    Advances in Partial Differential Equations 4.
    Akademie Verlag, Berlin, 1997.
    (Editor together with E. Schrohe, B.-W. Schulze and J. Sjöstrand)
  5. Evolution Equations, Fesbach Resonances, Singular Hogde Theory.
    Advances in Partial Differential Equations 5.
    Wiley-VCH, Weinheim, 1999.
    (Editor together with E. Schrohe, B.-W. Schulze and J. Sjöstrand)
  6. Parabolicity, Volterra Calculus, and Conical Singularities.
    Advances in Partial Differential Equations 6.
    In Operator Theory, Advances and Applications, Vol. 138
    Birkhäuser Verlag, Basel, 2002.
    (Editor together with S. Albeverio, E. Schrohe, B.-W. Schulze)
  7. Nonlinear Hyperbolic Equations, Spectral Theory, and Wavelet
    Transformations.
    Advances in Partial Differential Equations 7.
    In Operator Theory, Advances and Applications, Vol. 145
    Birkhäuser Verlag, Basel, 2003.
    (Editor together with S. Albeverio, E. Schrohe, B.-W. Schulze)
  8. Aspects of Boundary Problems in Analysis and Geometry.
    Advances in Partial Differential Equations 8.
    In Operator Theory, Advances and Applications, Vol. 151
    Birkhäuser Verlag, Basel, 2004.
    (Editor together with S. Albeverio, E. Schrohe, B.-W. Schulze)
  9. Symplectic Geometry and Quantum Mechanics.
    Advances in Partial Differential Equations 9.
    In Operator Theory, Advances and Applications, Vol. 166
    Birkhäuser Verlag, Basel, 2006.
    (Editor together with S. Albeverio, J. A. Goldstein,
    B.-W. Schulze and N. Tose)
  10. Elliptic Theory and Noncommutative Geometry.
    Advances in Partial Differential Equations 10.
    In Operator Theory, Advances and Applications, Vol. 183
    Birkhäuser Verlag, Basel, 2008.
    (Editor together with S. Albeverio, J. A. Goldstein,
    B.-W. Schulze and N. Tose)
  11. Nonlinear Parabolic-Hyperbolic Coupled Systems and Their Attractors
    Advances in Partial Differential Equations 11.
    In Operator Theory, Advances and Applications, Vol. 184
    Birkhäuser Verlag, Basel, 2008.
    (Editor together with S. Albeverio, J. A. Goldstein,
    B.-W. Schulze and N. Tose)
  12. Partial Differential Equations and Spectral Theory
    Advances in Partial Differential Equations 12.
    In Operator Theory, Advances and Applications, Vol 211
    Birkhäuser Verlag, Basel 2011
    (Editor with B.-W. Schulze and I. Witt)
  13. Mathematical Physics, Spectral Theory and Stochastic Analysis
    Advances in Partial Differential Equations 13.
    In Operator Theory, Advances and Applications, Vol 232
    Birkhäuser Verlag, Basel 2013
    (Editor with W. Kirsch)