Publications
2006
- G. Teschl, On the approximation of isolated eigenvalues of ordinary differential operators, Proc. Amer. Math. Soc. 136, 2473-2476 (2008).
2007
- 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).
- 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.
- A. Sakhnovich, Bäcklund-Darboux transformation for non-isospectral canonical system and Riemann-Hilbert problem, SIGMA 3, 054 (2007).
- 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).
- 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).
- S. Kamvissis and G. Teschl, Long-time asymptotics of the periodic Toda lattice under short-range perturbations, Preprint.
- 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).
- H. Krüger and G. Teschl, Relative oscillation theory for Sturm-Liouville operators extended, J. Funct. Anal. 254-6, 1702-1720 (2008).
- 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).
- A. Sakhnovich, Weyl functions, inverse problem and special solutions for the system auxiliary to the nonlinear optics equation, Inverse Problems 24 (2008) 025026.
- H. Krüger and G. Teschl, Effective Prüfer angles and relative oscillation criteria, J. Diff. Eq. 245, 3823-3848 (2008).
- 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).
- 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.
- A. Sakhnovich, Nonisospectral integrable nonlinear equations with external potentials and their GBDT solutions, J. Phys. A: Math. Theor. 41, 155204 (2008)
- 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).
- H. Krüger and G. Teschl, Long-time asymptotics for the Toda lattice in the soliton region, Math. Z. 262, 585-602 (2009).
- 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).
- 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.
- 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
- 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).
- 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).
- 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.
- 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).
- S. Kamvissis and G. Teschl, Stability of the periodic Toda lattice: Higher order asymptotics, Preprint.
- 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).
- 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).
- 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.
- 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).
- I. Egorova and G. Teschl, Reconstruction of the transmission coefficient for steplike finite-gap backgrounds, Oper. Matrices 3, 205-214 (2009).
- 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.
- 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
- G. Teschl, Mathematical Methods in Quantum Mechanics; With Applications to Schrödinger Operators, Graduate Studies in Mathematics 99, Amer. Math. Soc., Providence, 2009.
- G. Teschl, On the spatial asymptotics of solutions of the Toda lattice, Discrete Contin. Dyn. Syst. 27:3, 1233-1239 (2010).
- 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).
- 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.
- 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).
- H. Krüger and G. Teschl, Unique continuation for discrete nonlinear wave equations, Proc. Amer. Math. Soc. 140, 1321-1330 (2012).
- 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).
- 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).
- 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).
- 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).
- 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).
- 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).
- 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).
- 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).
- 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).
- 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
- A.L. Sakhnovich, Sine-Gordon theory in a semi-strip, Nonlinear Analysis 75, 964-974 (2012).
- 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).
- R. Stadler and G. Teschl, Relative oscillation theory for Dirac operators, J. Math. Anal. Appl. 371, 638-648 (2010).
- 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).
- A. Kostenko, A.L. Sakhnovich, and G. Teschl, Inverse eigenvalue problems for perturbed spherical Schrödinger operators, Inverse Problems 26, 105013, 14pp (2010).
- K. Grunert, H. Holden, and X. Raynaud, Lipschitz metric for the periodic Camassa-Holm equation, J. Diff. Eq. 250, 1460-1492 (2011).
- K. Grunert, The transformation operator for one-dimensional Schrödinger operators on almost periodic infinite-gap backgrounds, J. Diff. Eq. 250, 3534-3558 (2011).
- 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).
- 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).
- A. Kostenko and G. Teschl, On the singular Weyl-Titchmarsh function of perturbed spherical Schrödinger operators, J. Diff. Eq. 250, 3701-3739 (2011).
- 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).
- 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).
- K. Grunert, H. Holden, and X. Raynaud, Lipschitz metric for the Camassa-Holm equation on the line, Discrete and Continuous Dynamical Systems (to appear).
- A.L. Sakhnovich, On the factorization formula for fundamental solutions in the inverse spectral transform, J. Differential Equations 252, 3658-3667 (2012).
- A. Kostenko, A.L. Sakhnovich, and G. Teschl, Commutation methods for Schrödinger operators with strongly singular potentials, Math. Nachr. 285, 392-410 (2012).
- 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
- 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).
- J. Eckhardt and G. Teschl, On the connection between the Hilger and Radon-Nikodym derivatives, J. Math. Anal. Appl. 385, 1184-1189 (2012).
- N. Falkner and G. Teschl, On the substitution rule for Lebesgue-Stieltjes integrals, Preprint.
- 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).
- 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).
- 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.
- 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).
- J. Eckhardt and G. Teschl, Sturm-Liouville operators with measure-valued coefficients, J. d'Analyse Math. (to appear).
- J. Eckhardt and G. Teschl, Sturm-Liouville operators on time scales, J. Difference Equ. Appl. (to appear).
- J. Eckhardt, Schrödinger operators with strongly singular potentials and de Branges spaces, Preprint.
- B. Fritzsche, B. Kirstein, I.Ya. Roitberg, and A.L. Sakhnovich, Operator identities corresponding to inverse problems, Preprint.
- 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).
- 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).
- A.L. Sakhnovich, KdV equation in the quarter-plane: evolution of the Weyl functions and unbounded solutions, Preprint.
- 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.
- J. Eckhardt and G. Teschl, Uniqueness results for one-dimensional Schrödinger operators with purely discrete spectra, Trans. Amer. Math. Soc. (to appear).
- J. Eckhardt, Direct and inverse spectral theory of singular left-definite Sturm-Liouville operators, Preprint.
- L. Grafakos and G. Teschl, On Fourier transforms of radial functions and distributions, J. Fourier Anal. Appl. (to appear).
- 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
- I. Egorova, J. Michor, and G. Teschl, Scattering theory with finite-gap backgrounds: Transformation operators and characteristic properties of scattering data, Preprint.
- 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
- J. Eckhardt, Inverse spectral problems for a class of singular Krein strings, Preprint.
- 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).
- 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.
- J. Eckhardt and G. Teschl, Singular Weyl-Titchmarsh-Kodaira theory for Jacobi operators, Oper. Matrices (to appear).
- K. Grunert, Scattering theory for Schrödinger operators on steplike, almost periodic infinite-gap backgrounds, Preprint.
- U. Islambekov, R. Sims, and G. Teschl, Lieb-Robinson bounds for the Toda lattice, Preprint.
- J. Eckhardt, F. Gesztesy, R. Nichols, and G. Teschl, Weyl-Titchmarsh theory for Sturm-Liouville operators with distributional coefficients, Preprint.
- A. Kostenko and G. Teschl, Spectral asymptotics for perturbed spherical Schrödinger operators and applications to quantum scattering, Preprint.
Theses
Diploma theses
- Helge Krüger, Relative Oscillation Theory for Sturm-Liouville Operators, December 2006 (awarded the Studienpreis of the Austrian Mathematical Society 2008)
- Michael Schmied, Spectral Theory for Schrödinger Operators on Regular Tree Graphs, June 2007
- Katrin Grunert, Long-time Asymptotics for the Korteweg-de Vries Equation, May 2008 (awarded the Studienpreis of the Austrian Mathematical Society 2009)
- Kerstin Ammann, Relative Oscillation Theory for Jacobi Operators, November 2008
- Robert Stadler, Relative Oscillation Theory for Dirac Operators, February 2010
PhD theses
- Alice Mikikits-Leitner, Long-Time Asymptotics for the Asymtotically Periodic Korteweg-de Vries Equation, December 2009
- 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)
- Julian King, Mathematical Modeling of Blood-Gas Kinetics for the Volatile Organic Compounds Isoprene and Acetone, November 2010
- Helin Koç Rauchenwald, Compartmental Modeling for the Volatile Organic Compound Isoprene in Human Breath, September 2011
- Jonathan Eckhardt, On the isospectral problem of the Camassa-Holm equation, November 2011
