Institut für Angewandte Mathematik (Math D)
Publications of Markus Holzmann
Homepage of Markus Holzmann
Refereed publications
  1. J. Behrndt, M. Holzmann, V. Lotoreichik, G. Raikov:
    The fate of Landau levels under δ-interactions,
    accepted for publication in J. Spectral Theory; arXiv.

  2. P. Exner, M. Holzmann:
    Dirac operator spectrum in tubes and layers with a zigzag type boundary,
    Lett. Math. Phys. 112 (2022), Art. 102 (23 pages); arXiv.

  3. J. Behrndt, M. Holzmann, M. Tusek:
    Spectral transition for Dirac operators with electrostatic δ-shell potentials supported on the straight line,
    Integral Equations Operator Theory 94 (2022), Art. 33 (13 pages); arXiv.

  4. M. Holzmann:
    A note on the three dimensional Dirac operator with zigzag type boundary conditions,
    Complex Anal. Oper. Theory 15 (2021), Art. 47 (15 pages); arXiv.

  5. M. Holzmann, G. Unger:
    Boundary integral formulations of eigenvalue problems for elliptic differential operators with singular interactions and their numerical approximation by boundary element methods,
    Oper. Matrices 14 (3) (2020), 555-599; arXiv.

  6. J. Behrndt, M. Holzmann, T. Ourmieres-Bonafos, K. Pankrashkin:
    Two-dimensional Dirac operators with singular interactions supported on closed curves,
    J. Funct. Anal. 279 (8) (2020), 108700 (47 pages); arXiv.

  7. J. Behrndt, M. Holzmann, A. Mas:
    Self-adjoint Dirac operators on domains in R^3,
    Ann. Henri Poincare 21 (2020), 2681-2735; arXiv.

  8. J. Behrndt, M. Holzmann, A. Mantile, A. Posilicano:
    Limiting absorption principle and scattering matrix for Dirac operators with δ-shell interactions,
    J. Math. Phys. 61 (2020), 033504 (16 pages); arXiv.

  9. J. Behrndt, P. Exner, M. Holzmann, V. Lotoreichik:
    The Landau Hamiltonian with δ-potentials supported on curves,
    Rev. Math. Phys. 32 (4) (2020), 2050010 (51 pages); arXiv.

  10. J. Behrndt, M. Holzmann:
    On Dirac operators with electrostatic δ-shell interactions of critical strength,
    J. Spectral Theory 10 (1) (2020), 147-184; arXiv.

  11. J. Behrndt, P. Exner, M. Holzmann, V. Lotoreichik:
    On Dirac operators in R^3 with electrostatic and Lorentz scalar δ-shell interactions,
    Quantum Stud.: Math. Found. 6 (3) (2019), 295-314; arXiv.

  12. M. Holzmann, V. Lotoreichik:
    Spectral analysis of photonic crystals made of thin rods,
    Asymptot. Anal. 110 (1-2) (2018), 83-112; arXiv.

  13. M. Holzmann, T. Ourmieres-Bonafos, K. Pankrashkin:
    Dirac operators with Lorentz scalar shell interactions,
    Rev. Math. Phys. 30 (2018), 1850013 (46 pages); arXiv.

  14. J. Behrndt, P. Exner, M. Holzmann, V. Lotoreichik:
    On the spectral properties of Dirac operators with electrostatic δ-shell interactions,
    J. Math. Pures Appl. 111 (2018), 47-78; arXiv.

  15. J. Behrndt, P. Exner, M. Holzmann, V. Lotoreichik:
    Approximation of Schrödinger operators with δ-interactions supported on hypersurfaces,
    Math. Nachr. 290 (2017), 1215–1248; arXiv.

Submitted papers
  1. J. Behrndt, M. Holzmann, C. Stelzer, G. Stenzel:
    Boundary triples and Weyl functions for Dirac operators with singular interactions, arXiv.

  2. J. Behrndt, M. Holzmann, M. Tusek:
    Two-dimensional Dirac operators with general δ-shell interactions supported on a straight line, arXiv.

  3. J. Behrndt, M. Holzmann, G. Stenzel:
    Schrödinger operators with oblique transmission conditions in R^2, arXiv.

Other publications
  1. J. Behrndt, M. Holzmann, C. Stelzer, G. Stenzel:
    A class of singular perturbations of the Dirac operator: boundary triplets and Weyl functions,
    Acta Wasaensia 462 (2021), Festschrift in honor of Seppo Hassi, 15-36.

  2. M. Holzmann:
    The nonrelativistic limit of Dirac operators with Lorentz scalar δ-shell interactions,
    Proc. Appl. Math. Mech. 19 (2019), e201900126 (2 pages).

  3. J. Behrndt, M. Holzmann, V. Lotoreichik:
    Convergence of 2D-Schrödinger operators with local scaled short-range interactions to a Hamiltonian with infinitely many δ-point interactions,
    Proc. Appl. Math. Mech. 14 (2014), 1005–1006.
Thesis
  1. M. Holzmann,
    Spectral Analysis of Transmission and Boundary Value Problems for Dirac Operators,
    PhD. Thesis, TU Graz, 2018.
  2. M. Holzmann,
    Approximation of Schrödinger operators with δ-interactions supported on hypersurfaces,
    Master Thesis, TU Graz, 2014, pdf.