Block Operator Techniken für Systeme partieller Differentialgleichungen und Anwendungen in der Mathematischen Physik

• Applicant: Professorin Dr. Christiane Tretter
• Subject Area: Mathematics
• Term: from 2004 to 2008
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 5441440

• Final Report Year: 2013

Final Report Abstract

No abstract available

Publications

• The angular part of the Dirac operator in Kerr-Newman spacetime: Estimates for the eigenvalues. Dissertation, Universität Bremen, 2005, 154 S.
  Winklmeier, M.
  
• Spectral theory of the Klein-Gordon equation in Pontryagin spaces. Communications in Mathematical Physics, Vol. 267. 2006, Issue 1, pp. 159-180.
  Langer, H., Najman, B., Tretter, C.
  (See online at https://dx.doi.org/10.1007/s00220-006-0022-4)
• Variational principles for eigenvalues of the Klein-Gordon equation. Journal of Mathematical Physics, Vol. 47. 2006, Issue 10: 103506.
  Langer, M., Tretter, C.
  (See online at https://dx.doi.org/10.1063/1.2345108)
• Block numerical ranges. Dissertation, Fachbereich 3 (Mathematik & Informatik) der Universität Bremen, 2007, 88 S.
  Wagenhofer, M.
  
• Spectral Theory of Block Operator Matrices and Applications. Imperial College Press, London, 2008.
  Tretter, C.
  (See online at https://dx.doi.org/10.1142/9781848161122_fmatter)
• Spectral theory of the Klein-Gordon equation in Krein spaces. Proceedings of the Edinburgh Mathematical Society (Series 2), Volume 51. 2008, Issue 3, pp. 711-750.
  Langer, H., Najman, B., Tretter, C.
  (See online at https://dx.doi.org/10.1017/S0013091506000150)
• A spectral approach to the Dirac equation in the non-extreme Kerr-Newmann metric. Journal of Physics A: Mathematical and Theoretical, Vol. 42. 2009, Number 29, 295204.
  Winklmeier, M., Yamada, O.
  (See online at https://dx.doi.org/10.1088/1751-8113/42/29/295204)
• Spectral inclusion for unbounded block operator matrices. Journal of Functional Analysis, Vol. 256. 2009, Issue 11, pp. 3806–3829.
  Tretter, C.
  (See online at https://dx.doi.org/10.1016/j.jfa.2008.12.024)
• On the spectrum of the magnetohydrodynamic mean-field 2-dynamo operator. SIAM Journal on Mathematical Analysis, Vol. 42. 2010, Issue 3, pp. 1413-1447.
  Günther, U., Langer, H., Tretter, C.
  (See online at https://dx.doi.org/10.1137/100782024)
• PT-symmetric Schr¨odinger operators with unbounded potentials. Dissertation Universität Bern, 2010.
  Nesemann, J.
  (See online at https://dx.doi.org/10.1007/978-3-8348-8327-8)
• The quadratic numerical range of an analytic operator function. Complex Analysis and Operator Theory, Vol. 4. 2010, Issue 2, pp. 449-469.
  Tretter, C.
  (See online at https://dx.doi.org/10.1007/s11785-009-0019-z)
• Block-diagonalization of operators with gaps, with applications to Dirac operators. Reviews in Mathematical Physics, Vol. 24. 2012, Issue 8, 1250021.
  Cuenin, J.-C.
  (See online at https://doi.org/10.1142/S0129055X12500213)
• Essential spectrum of systems of singular differential equations. Acta Scientiarum Mathematicarum (Szeged), Vol. 79. 2013, Issue 3/4, pp. 423–465.
  Ibrogimov, O., Langer, H., Langer, M., Tretter, C.
  
• Spectral bounds and basis results for non-selfadjoint pencils, with an application to Hagen–Poiseuille flow. Journal of Functional Analysis, Vol. 264. 2013, Issue 9, pp. 2136–2176.
  Marletta, M., Tretter, C.
  (See online at https://doi.org/10.1016/j.jfa.2013.02.008)
• The block numerical range of analytic operator functions. Preprint, 19 pp., 2013. Operators and Matrices, Vol. 8.2014, Number 4, pp. 901–934.
  Radl, A., Tretter, C., Wagenhofer, M.
  (See online at https://dx.doi.org/10.7153/oam-08-51)
• Dichotomous Hamiltonians with unbounded entries and solutions of Riccati equations. Journal of Evolution Equations, Vol. 14. 2014, Issue 1, pp 121-153.
  Tretter, C., Wyss, C.
  (See online at https://doi.org/10.1007/s00028-013-0210-6)
• Eigenvalue estimates for non-self-adjoint Dirac operators on the real line. Annales Henri Poincaré, Vol. 15. 2014, Issue 4, pp. 707-736.
  Cuenin, J.-C., Laptev, A., Tretter, C.
  (See online at https://doi.org/10.1007/s00023-013-0259-3)