Publications

2006

  1. G. Teschl, On the approximation of isolated eigenvalues of ordinary differential operators, Proc. Amer. Math. Soc. 136, 2473-2476 (2008).

2007

  1. F. Gesztesy, H. Holden, J. Michor, and G. Teschl, Algebro-geometric finite-band solutions of the Ablowitz-Ladik hierarchy, Int. Math. Res. Not. 2007, no. 20, Art. ID rnm082, 55pp (2007).
  2. F. Gesztesy, H. Holden, J. Michor, and G. Teschl, The Ablowitz-Ladik hierarchy revisited, in Methods of Spectral Analysis in Mathematical Physics, J. Janas (ed.) et al., 139-190, Oper. Theory Adv. Appl. 186, Birkhäuser, Basel, 2009.
  3. A. Sakhnovich, Bäcklund-Darboux transformation for non-isospectral canonical system and Riemann-Hilbert problem, SIGMA 3, 054 (2007).
  4. B. Fritzsche, B. Kirstein, I.Ya. Roitberg, A.L. Sakhnovich, Weyl matrix functions and inverse problems for discrete Dirac type self-adjoint system: explicit and general solutions, Oper. Matrices 2, 201-231 (2008).
  5. H. Krüger and G. Teschl, Relative oscillation theory, weighted zeros of the Wronskian, and the spectral shift function, Commun. Math. Phys. 287:2, 613-640 (2009).
  6. S. Kamvissis and G. Teschl, Long-time asymptotics of the periodic Toda lattice under short-range perturbations, Preprint.
  7. F. Gesztesy, H. Holden, J. Michor, and G. Teschl, The algebro-geometric initial value problem for the Ablowitz-Ladik hierarchy, Discrete Contin. Dyn. Syst. 26:1, 151-196 (2010).
  8. H. Krüger and G. Teschl, Relative oscillation theory for Sturm-Liouville operators extended, J. Funct. Anal. 254-6, 1702-1720 (2008).
  9. A. Boutet de Monvel, I. Egorova, and G. Teschl, Inverse scattering theory for one-dimensional Schrödinger operators with steplike finite-gap potentials, J. d'Analyse Math. 106:1, 271-316 (2008).
  10. A. Sakhnovich, Weyl functions, inverse problem and special solutions for the system auxiliary to the nonlinear optics equation, Inverse Problems 24 (2008) 025026.
  11. H. Krüger and G. Teschl, Effective Prüfer angles and relative oscillation criteria, J. Diff. Eq. 245, 3823-3848 (2008).
  12. I. Egorova, J. Michor, and G. Teschl, Scattering theory for Jacobi operators with general steplike quasi-periodic background, Zh. Mat. Fiz. Anal. Geom. 4-1, 33-62 (2008).
  13. J. Michor and G. Teschl, On the equivalence of different Lax pairs for the Kac-van Moerbeke hierarchy, in Modern Analysis and Applications, V. Adamyan (ed.) et al., 445-453, Oper. Theory Adv. Appl. 191, Birkhäuser, Basel, 2009.
  14. A. Sakhnovich, Nonisospectral integrable nonlinear equations with external potentials and their GBDT solutions, J. Phys. A: Math. Theor. 41, 155204 (2008)
  15. F. Gesztesy, H. Holden, J. Michor, and G. Teschl, Local conservation laws and the Hamiltonian formalism for the Ablowitz-Ladik hierarchy, Stud. Appl. Math. 120-4, 361-423 (2008).
  16. H. Krüger and G. Teschl, Long-time asymptotics for the Toda lattice in the soliton region, Math. Z. 262, 585-602 (2009).
  17. M. Schmied, R. Sims, and G. Teschl, On the absolutely continuous spectrum of Sturm-Liouville operators with applications to radial quantum trees, Oper. Matrices 2:3, 417-434 (2008).
  18. B. Nachtergaele and R. Sims, Locality estimates for quantum spin systems, in New Trends in Mathematical Physics. Selected contributions of the XVth International Congress on Mathematical Physics, V. Sidoravicius (ed.), 591-614, Springer Verlag, 2009.
  19. B. Nachtergaele, H. Raz, B. Schlein, and R. Sims Lieb-Robinson bounds for harmonic and anharmonic lattice systems, Comm. Math. Phys. 286, 1073-1098 (2009).

2008

  1. A.L. Sakhnovich and L.A. Sakhnovich, On a mean value theorem in the class of Herglotz functions and its applications, ELA 17, 102-109 (2008).
  2. B. Fritzsche, B. Kirstein, and A.L. Sakhnovich, On a new class of structured matrices related to the discrete skew-self-adjoint Dirac systems, ELA 17, 473-486 (2008).
  3. D. Alpay, I. Gohberg, M.A. Kaashoek, L. Lerer, and A. Sakhnovich, Krein systems, in Modern Analysis and Applications, V. Adamyan (ed.) et al., 19-36, Oper. Theory Adv. Appl. 191, Birkhäuser, Basel, 2009.
  4. H. Krüger and G. Teschl, Long-time asymptotics of the Toda lattice for decaying initial data revisited, Rev. Math. Phys. 21:1, 61-109 (2009).
  5. S. Kamvissis and G. Teschl, Stability of the periodic Toda lattice: Higher order asymptotics, Preprint.
  6. H. Krüger and G. Teschl, Stability of the periodic Toda lattice in the soliton region, Int. Math. Res. Not. 2009, Art. ID rnp077, 36pp (2009).
  7. K. Grunert and G. Teschl, Long-time asymptotics for the Korteweg-de Vries Equation via nonlinear steepest descent, Math. Phys. Anal. Geom. 12, 287-324 (2009).
  8. F. Gesztesy, H. Holden, J. Michor, and G. Teschl, Soliton Equations and Their Algebro-Geometric Solutions. Volume II: (1+1)-Dimensional Discrete Models, Cambridge Studies in Advanced Mathematics 114, Cambridge University Press, Cambridge, 2008.
  9. F. Gesztesy, M. Malamud, M. Mitrea, and S. Naboko, Generalized Polar Decompositions for Closed Operators in Hilbert Spaces and Some Applications, Integr. equ. oper. theory 64 , 83-113 (2009).
  10. I. Egorova and G. Teschl, Reconstruction of the transmission coefficient for steplike finite-gap backgrounds, Oper. Matrices 3, 205-214 (2009).
  11. K. Ammann and G. Teschl, Relative oscillation theory for Jacobi matrices, in Proceedings of the 14th International Conference on Difference Equations and Applications, M. Bohner (ed) et al., 105-115, Uğur-Bahçeşehir University Publishing Company, Istanbul, 2009.
  12. K. Grunert, I. Egorova, and G. Teschl, On the Cauchy problem for the Korteweg-de Vries equation with steplike finite-gap initial data I. Schwarz-type perturbations, Nonlinearity 22, 1431-1457 (2009).

2009

  1. G. Teschl, Mathematical Methods in Quantum Mechanics; With Applications to Schrödinger Operators, Graduate Studies in Mathematics 99, Amer. Math. Soc., Providence, 2009.
  2. G. Teschl, On the spatial asymptotics of solutions of the Toda lattice, Discrete Contin. Dyn. Syst. 27:3, 1233-1239 (2010).
  3. A. Boutet de Monvel, A. Kostenko, D. Shepelsky, and G. Teschl, Long-time asymptotics for the Camassa-Holm equation, SIAM J. Math. Anal. 41:4, 1559-1588 (2009).
  4. A. Mikikits-Leitner and G. Teschl, Trace formulas for Schrödinger operators in connection with scattering theory for finite-gap backgrounds, in Spectral Theory and Analysis, J. Janas (ed.) et al., 107-124, Oper. Theory Adv. Appl. 214, Birkhäuser, Basel, 2011.
  5. M. Ashbaugh, F. Gesztesy, M. Mitrea, R. Shterenberg, and G. Teschl, The Krein-von Neumann extension and its connection to an abstract buckling problem, Math. Nachr. 283:2, 165-179 (2010).
  6. H. Krüger and G. Teschl, Unique continuation for discrete nonlinear wave equations, Proc. Amer. Math. Soc. 140, 1321-1330 (2012).
  7. B. Fritzsche, B. Kirstein, and A.L. Sakhnovich, Semiseparable integral operators and explicit solution of an inverse problem for the skew-self-adjoint Dirac-type system, Integr. Equ. Oper. Theory 66, 231-251 (2010).
  8. J. King, A. Kupferthaler, K. Unterkofler, H. Koc, S. Teschl, G. Teschl, W. Miekisch, J. Schubert, H. Hinterhuber, and A. Amann, Isoprene and acetone concentration profiles during exercise on an ergometer, J. Breath Res. 3, 027006, 16pp (2009).
  9. A.L. Sakhnovich, A.A. Karelin, J. Seck-Tuoh-Mora, G. Perez-Lechuga, M. Gonzalez-Hernandez, On explicit inversion of a subclass of operators with D-difference kernels and Weyl theory of the corresponding canonical systems, Positivity 14:3, 547-564 (2010).
  10. I. Egorova, J. Michor, and G. Teschl, Inverse scattering transform for the Toda hierarchy with steplike finite-gap backgrounds, J. Math. Phys. 50, 103521 (2009).
  11. M. Ashbaugh, F. Gesztesy, M. Mitrea, and G. Teschl, Spectral theory for perturbed Krein Laplacians in non-smooth domains, Adv. Math. 223, 1372-1467 (2010).
  12. I. Egorova and G. Teschl, On the Cauchy problem for the Korteweg-de Vries equation with steplike finite-gap initial data II. Perturbations with finite moments, J. d'Analyse Math. 115:1, 71-101 (2011).
  13. I. Egorova and G. Teschl, A Paley-Wiener theorem for periodic scattering with applications to the Korteweg-de Vries equation, Zh. Mat. Fiz. Anal. Geom. 6:1, 21-33 (2010).
  14. A.L. Sakhnovich, On the GBDT version of the Bäcklund-Darboux transformation and its applications to the linear and nonlinear equations and spectral theory, Math. Model. Nat. Phenom. 5:4, 340-389 (2010).
  15. I. Egorova and G. Teschl, On the Cauchy problem for the modified Korteweg-de Vries equation with steplike finite-gap initial data, Proceedings of the International Research Program on Nonlinear PDE, H. Holden and K. H. Karlsen (eds), 151-158, Contemp. Math. 526, Amer. Math. Soc., Providence (2010).
  16. D. Alpay, I. Gohberg, M.A. Kaashoek, L. Lerer, A.L. Sakhnovich, Krein systems and canonical systems on a finite interval: accelerants with a jump discontinuity at the origin and continuous potentials, Integr. Equ. Oper. Theory 68:1, 115-150 (2010).

2010

  1. A.L. Sakhnovich, Sine-Gordon theory in a semi-strip, Nonlinear Analysis 75, 964-974 (2012).
  2. A.L. Sakhnovich, Construction of the solution of the inverse spectral problem for a system depending rationally on the spectral parameter, Borg-Marchenko-type theorem, and sine-Gordon equation, Integr. Equ. Oper. Theory 69, 567-600 (2011).
  3. R. Stadler and G. Teschl, Relative oscillation theory for Dirac operators, J. Math. Anal. Appl. 371, 638-648 (2010).
  4. J. King, K. Unterkofler, G. Teschl, S. Teschl, H. Koc, H. Hinterhuber, and A. Amann, A mathematical model for breath gas analysis of volatile organic compounds with special emphasis on acetone, J. Math. Biol. 63, 959-999 (2011).
  5. A. Kostenko, A.L. Sakhnovich, and G. Teschl, Inverse eigenvalue problems for perturbed spherical Schrödinger operators, Inverse Problems 26, 105013, 14pp (2010).
  6. K. Grunert, H. Holden, and X. Raynaud, Lipschitz metric for the periodic Camassa-Holm equation, J. Diff. Eq. 250, 1460-1492 (2011).
  7. K. Grunert, The transformation operator for one-dimensional Schrödinger operators on almost periodic infinite-gap backgrounds, J. Diff. Eq. 250, 3534-3558 (2011).
  8. A. Kostenko, A.L. Sakhnovich, and G. Teschl, Weyl-Titchmarsh theory for Schrödinger operators with strongly singular potentials, Int. Math. Res. Not. 2012, 1699-1747 (2012).
  9. B. Fritzsche, B. Kirstein, and A.L. Sakhnovich, Weyl functions of generalized Dirac systems: Integral representation, the inverse problem and discrete interpolation, J. Anal. Math. 116, 17-51 (2012).
  10. A. Kostenko and G. Teschl, On the singular Weyl-Titchmarsh function of perturbed spherical Schrödinger operators, J. Diff. Eq. 250, 3701-3739 (2011).
  11. J. King, H. Koc, K. Unterkofler, P. Mochalski, A. Kupferthaler, G. Teschl, S. Teschl, H. Hinterhuber, and A. Amann Physiological modeling of isoprene dynamics in exhaled breath, J. Theoret. Biol. 267, 626-637 (2010).
  12. A. Mikikits-Leitner and G. Teschl, Long-time asymptotics of perturbed finite-gap Korteweg-de Vries solutions, J. d'Analyse Math. 116, 163-218 (2012).
  13. K. Grunert, H. Holden, and X. Raynaud, Lipschitz metric for the Camassa-Holm equation on the line, Discrete and Continuous Dynamical Systems (to appear).
  14. A.L. Sakhnovich, On the factorization formula for fundamental solutions in the inverse spectral transform, J. Differential Equations 252, 3658-3667 (2012).
  15. A. Kostenko, A.L. Sakhnovich, and G. Teschl, Commutation methods for Schrödinger operators with strongly singular potentials, Math. Nachr. 285, 392-410 (2012).
  16. F. Gesztesy, J. A. Goldstein, H. Holden, and G. Teschl, Abstract wave equations and associated Dirac-type operators, Ann. Mat. Pura Appl. (to appear).

2011

  1. H. Koc, J. King, G. Teschl, K. Unterkofler, S. Teschl, P. Mochalski, H. Hinterhuber, and A. Amann, The role of mathematical modeling in VOC analysis using isoprene as a prototypic example, J. Breath Res. 5, 037102, 9pp (2011).
  2. J. Eckhardt and G. Teschl, On the connection between the Hilger and Radon-Nikodym derivatives, J. Math. Anal. Appl. 385, 1184-1189 (2012).
  3. N. Falkner and G. Teschl, On the substitution rule for Lebesgue-Stieltjes integrals, Preprint.
  4. A.L. Sakhnovich, Time-dependent Schrödinger equation in dimension k+1: explicit and rational solutions via GBDT and multinodes, J. Phys. A: Math. Theor. 44, 475201 (2011).
  5. J. King, K. Unterkofler, G. Teschl, S. Teschl, P. Mochalski, H. Koc, H. Hinterhuber, and A. Amann, A modeling-based evaluation of isothermal rebreathing for breath gas analyses of highly soluble volatile organic compounds, J. Breath Res. 6, 016005, 11pp (2012).
  6. B. Fritzsche, B. Kirstein, I.Ya. Roitberg, and A.L. Sakhnovich, Weyl theory and explicit solutions of direct and inverse problems for a Dirac system with rectangular matrix potential, Preprint.
  7. J. King, A. Kupferthaler, B. Frauscher, H. Hackner, K. Unterkofler, G. Teschl, H. Hinterhuber, A. Amann, and B. Högl, Measurement of endogenous acetone and isoprene in exhaled breath during sleep, Physiol. Meas. 33, 413-428 (2012).
  8. J. Eckhardt and G. Teschl, Sturm-Liouville operators with measure-valued coefficients, J. d'Analyse Math. (to appear).
  9. J. Eckhardt and G. Teschl, Sturm-Liouville operators on time scales, J. Difference Equ. Appl. (to appear).
  10. J. Eckhardt, Schrödinger operators with strongly singular potentials and de Branges spaces, Preprint.
  11. B. Fritzsche, B. Kirstein, I.Ya. Roitberg, and A.L. Sakhnovich, Operator identities corresponding to inverse problems, Preprint.
  12. B. Fritzsche, B. Kirstein, I.Ya. Roitberg, and A.L. Sakhnovich, Recovery of Dirac system from the rectangular Weyl matrix function, Inverse Problems 28, 015010, 18pp (2012).
  13. K. Grunert, H. Holden, and X. Raynaud, Global conservative solutions of the Camassa-Holm equation for initial data with nonvanishing asymptotics, Discrete Contin. Dyn. Syst. (to appear).
  14. A.L. Sakhnovich, KdV equation in the quarter-plane: evolution of the Weyl functions and unbounded solutions, Preprint.
  15. J. King, K. Unterkofler, S. Teschl, A. Amann, and G. Teschl, Breath gas analysis for estimating physiological processes using anesthetic monitoring as a prototypic example, Conf. Proc. IEEE Eng. Med. Biol. Soc. (2011), 1001-1004.
  16. J. Eckhardt and G. Teschl, Uniqueness results for one-dimensional Schrödinger operators with purely discrete spectra, Trans. Amer. Math. Soc. (to appear).
  17. J. Eckhardt, Direct and inverse spectral theory of singular left-definite Sturm-Liouville operators, Preprint.
  18. L. Grafakos and G. Teschl, On Fourier transforms of radial functions and distributions, J. Fourier Anal. Appl. (to appear).
  19. B. Fritzsche, B. Kirstein, I.Ya. Roitberg, and A.L. Sakhnovich, Skew-self-adjoint Dirac systems with a rectangular matrix potential: Weyl theory, direct and inverse problems, Preprint.

2012

  1. I. Egorova, J. Michor, and G. Teschl, Scattering theory with finite-gap backgrounds: Transformation operators and characteristic properties of scattering data, Preprint.
  2. A. Sakhnovich and L. Sakhnovich, The nonlinear Fokker-Planck equation: comparison of the classical and quantum (boson and fermion) characteristics, Journal of Physics: Conference Series 343 (2012) 012108
  3. J. Eckhardt, Inverse spectral problems for a class of singular Krein strings, Preprint.
  4. M. Shahriari, A. Jodayree Akbarfam, and G. Teschl, Uniqueness for inverse Sturm-Liouville problems with a finite number of transmission conditions, J. Math. Anal. Appl. (to appear).
  5. M.S. Ashbaugh, F. Gesztesy, M. Mitrea, R. Shterenberg, and G. Teschl, A survey on the Krein-von Neumann extension, the corresponding abstract buckling problem, and Weyl-type spectral asymptotics for perturbed Krein Laplacians in nonsmooth domains, Preprint.
  6. J. Eckhardt and G. Teschl, Singular Weyl-Titchmarsh-Kodaira theory for Jacobi operators, Oper. Matrices (to appear).
  7. K. Grunert, Scattering theory for Schrödinger operators on steplike, almost periodic infinite-gap backgrounds, Preprint.
  8. U. Islambekov, R. Sims, and G. Teschl, Lieb-Robinson bounds for the Toda lattice, Preprint.
  9. J. Eckhardt, F. Gesztesy, R. Nichols, and G. Teschl, Weyl-Titchmarsh theory for Sturm-Liouville operators with distributional coefficients, Preprint.
  10. A. Kostenko and G. Teschl, Spectral asymptotics for perturbed spherical Schrödinger operators and applications to quantum scattering, Preprint.
Theses

Diploma theses

  1. Helge Krüger, Relative Oscillation Theory for Sturm-Liouville Operators, December 2006 (awarded the Studienpreis of the Austrian Mathematical Society 2008)
  2. Michael Schmied, Spectral Theory for Schrödinger Operators on Regular Tree Graphs, June 2007
  3. Katrin Grunert, Long-time Asymptotics for the Korteweg-de Vries Equation, May 2008 (awarded the Studienpreis of the Austrian Mathematical Society 2009)
  4. Kerstin Ammann, Relative Oscillation Theory for Jacobi Operators, November 2008
  5. Robert Stadler, Relative Oscillation Theory for Dirac Operators, February 2010

PhD theses

  1. Alice Mikikits-Leitner, Long-Time Asymptotics for the Asymtotically Periodic Korteweg-de Vries Equation, December 2009
  2. Katrin Grunert, Scattering Theory and Cauchy Problems, June 2010 (Award of Excellence of the Austrian Ministry of Science 2010; Studienpreis of the Austrian Mathematical Society 2011)
  3. Julian King, Mathematical Modeling of Blood-Gas Kinetics for the Volatile Organic Compounds Isoprene and Acetone, November 2010
  4. Helin Koç Rauchenwald, Compartmental Modeling for the Volatile Organic Compound Isoprene in Human Breath, September 2011
  5. Jonathan Eckhardt, On the isospectral problem of the Camassa-Holm equation, November 2011
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