Publications

An abstract for each publication is available by selecting the corresponding link. All documents are available as TeX or PDF file as indicated via

http://www.mat.univie.ac.at/~gerald/ftp/

DVI and TeX files can be previewed with packages from http://www.tug.org and PDF files with Acrobat Reader from http://www.adobe.com.

If you have troubles downloading or typestting these files feel free to contact me. Most older files are also available from mp-arc and all newer ones from arxiv (front|author id). However, note that the files below are updated whenever I encounter a typo. You can also search MathSciNet, ZMATH, Scopus, ResearcherID, Google Scholar (query), or Microsoft Academic. A list of coauthors is available as well.

• A coupling problem for entire functions and its application to the long-time asymptotics of integrable wave equations with J. Eckhardt [TeX | PDF]
• Inverse uniqueness results for one-dimensional weighted Dirac operators, with J. Eckhardt and A. Kostenko [TeX | PDF]
• Singular Weyl-Titchmarsh-Kodaira theory for one-dimensional Dirac operators, with R. Brunnhuber, J. Eckhardt, and A. Kostenko [TeX | PDF]
• Supersymmetry and Schrödinger-type operators with distributional matrix-valued potentials, with J. Eckhardt, F. Gesztesy, and R. Nichols [TeX | PDF]

• Long-time asymptotics for the Korteweg-de Vries equation with steplike initial data, with I. Egorova, Z. Gladka, and V. Kotlyarov, Nonlinearity (to appear). [TeX | PDF]
• Inverse spectral theory for Sturm-Liouville operators with distributional potentials, with J. Eckhardt, F. Gesztesy, and R. Nichols, J. London Math. Soc. (to appear). [TeX | PDF]
• On the isospectral problem of the dispersionless Camassa-Holm equation, with J. Eckhardt, Adv. Math. 235, 469-495 (2013). [TeX | PDF]
• Weyl-Titchmarsh theory for Sturm-Liouville operators with distributional potentials, with J. Eckhardt, F. Gesztesy, and R. Nichols, Opuscula Math. 33, 467-563 (2013). [TeX | PDF]
• Spectral asymptotics for perturbed spherical Schrödinger operators and applications to quantum scattering, with A. Kostenko, Comm. Math. Phys. (to appear). [TeX | PDF]
• Scattering theory with finite-gap backgrounds: Transformation operators and characteristic properties of scattering data, with I. Egorova and J. Michor, Math. Phys. Anal. Geom. (to appear). [TeX | PDF]
• Lieb-Robinson bounds for the Toda lattice, with U. Islambekov and R. Sims, J. Stat. Phys. 148, 440-479 (2012). [TeX | PDF]
• On the substitution rule for Lebesgue-Stieltjes integrals, with N. Falkner, Expo. Math. 30, 412-418 (2012). [TeX | PDF]
• Breath isoprene: muscle dystrophy patients support the concept of a pool of isoprene in the periphery of the human body, with J. King, P. Mochalski, K. Unterkofler, G. T., M. Klieber, M. Stein, A. Amann, and M. Baumann, Biochem. Biophys. Res. Commun. 423, 526-530 (2012). [DOC | PDF]
• Long-time asymptotics of the periodic Toda lattice under short-range perturbations, with S. Kamvissis, J. Math. Phys. 53, 073706 (2012). [TeX | PDF]
• Singular Weyl-Titchmarsh-Kodaira theory for Jacobi operators, with J. Eckhardt, Oper. Matrices (to appear). [TeX | PDF]
• On Fourier transforms of radial functions and distributions, with L. Grafakos, J. Fourier Anal. Appl. 19, 167-179 (2013). [TeX | PDF]
• Uniqueness for inverse Sturm-Liouville problems with a finite number of transmission conditions with M. Shahriari and A. Jodayree Akbarfam, J. Math. Anal. Appl. 395, 19-29 (2012). [TeX | PDF]
• Sturm-Liouville operators with measure-valued coefficients, with J. Eckhardt, J. d'Analyse Math. (to appear). [TeX | PDF]
• Uniqueness results for one-dimensional Schrödinger operators with purely discrete spectra, with J. Eckhardt, Trans. Amer. Math. Soc. 365, 3923-3942 (2013). [TeX | PDF]
• Measurement of endogenous acetone and isoprene in exhaled breath during sleep, with J. King, A. Kupferthaler, B. Frauscher, H. Hackner, K. Unterkofler, G.T., H. Hinterhuber, A. Amann, and B. Högl, Physiol. Meas. 33, 413-428 (2012). [PDF]
• A modeling-based evaluation of isothermal rebreathing for breath gas analyses of highly soluble volatile organic compounds, with J. King, K. Unterkofler, G.T., S. Teschl, P. Mochalski, H. Koc, H. Hinterhuber, and A. Amann, J. Breath Res. 6, 016005, 11pp (2012). [TeX | PDF]
• Breath gas analysis for estimating physiological processes using anesthetic monitoring as a prototypic example, with J. King, K. Unterkofler, S. Teschl, A. Amann, and G.T., Conf. Proc. IEEE Eng. Med. Biol. Soc. (2011), 1001-1004. [TeX | PDF]
• Sturm-Liouville operators on time scales, with J. Eckhardt, J. Difference Equ. Appl. 18, 1875-1887 (2012). [TeX | PDF]
• On the connection between the Hilger and Radon-Nikodym derivatives, with J. Eckhardt, J. Math. Anal. Appl. 385, 1184-1189 (2012). [TeX | PDF]
• Weyl-Titchmarsh theory for Schrödinger operators with strongly singular potentials, with A. Kostenko and A. Sakhnovich, Int. Math. Res. Not. 2012, 1699-1747 (2012). [TeX | PDF]
• Abstract wave equations and associated Dirac-type operators, with F. Gesztesy, J. A. Goldstein, and H. Holden, Ann. Mat. Pura Appl. 191, 631-676 (2012). [TeX | PDF]
• Commutation methods for Schrödinger operators with strongly singular potentials, with A. Kostenko and A. Sakhnovich, Math. Nachr. 285, 392-410 (2012). [TeX | PDF]
• Unique continuation for discrete nonlinear wave equations, with H. Krüger, Proc. Amer. Math. Soc. 140, 1321-1330 (2012). [TeX | PDF]
• A mathematical model for breath gas analysis of volatile organic compounds with special emphasis on acetone, with J. King, K. Unterkofler, G.T., S. Teschl, H. Koc, H. Hinterhuber, and A. Amann, J. Math. Biol. 63, 959-999 (2011). [TeX | PDF]
• On the singular Weyl-Titchmarsh function of perturbed spherical Schrödinger operators, with A. Kostenko, J. Differential Equations 250, 3701-3739 (2011). [TeX | PDF]
• Physiological modeling of isoprene dynamics in exhaled breath, with J. King, H. Koc, K. Unterkofler, P. Mochalski, A. Kupferthaler, G.T., S. Teschl, H. Hinterhuber, and A. Amann, J. Theoret. Biol. 267, 626-637 (2010). [TeX | PDF]
• Long-time asymptotics of perturbed finite-gap Korteweg-de Vries solutions, with A. Mikikits-Leitner, J. d'Analyse Math. 116, 163-218 (2012). [TeX | PDF]
• Inverse eigenvalue problems for perturbed spherical Schrödinger operators, with A. Kostenko and A. Sakhnovich, Inverse Problems 26, 105013, 14pp (2010). [TeX | PDF]
• Relative oscillation theory for Dirac operators, with R. Stadler, J. Math. Anal. Appl. 371, 638-648 (2010). [TeX | PDF]
• On the Cauchy problem for the Korteweg-de Vries equation with steplike finite-gap initial data II. Perturbations with finite moments, with I. Egorova, J. d'Analyse Math. 115, 71-101 (2011). [TeX | PDF]
• On the Cauchy problem for the modified Korteweg-de Vries equation with steplike finite-gap initial data, with I. Egorova, 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). [TeX | PDF]
• On the spatial asymptotics of solutions of the Toda lattice, Discrete Contin. Dyn. Syst. 27:3, 1233-1239 (2010). [TeX | PDF]
• A Paley-Wiener theorem for periodic scattering with applications to the Korteweg-de Vries equation, with I. Egorova, Zh. Mat. Fiz. Anal. Geom. 6:1, 21-33 (2010). [TeX | PDF]
• Spectral theory for perturbed Krein Laplacians in non-smooth domains, with M. Ashbaugh, F. Gesztesy, and M. Mitrea, Adv. Math. 223, 1372-1467 (2010). [TeX | PDF]
• Trace formulas for Schrödinger operators in connection with scattering theory for finite-gap backgrounds, with A. Mikikits-Leitner, in Spectral Theory and Analysis, J. Janas (ed.) et al., 107-124, Oper. Theory Adv. Appl. 214, Birkhäuser, Basel, 2011. [TeX | PDF]
• Inverse scattering transform for the Toda hierarchy with steplike finite-gap backgrounds, with I. Egorova and J. Michor, J. Math. Phys. 50, 103521 (2009). [TeX | PDF]
• Long-time asymptotics for the Korteweg-de Vries equation via nonlinear steepest descent, with K. Grunert, Math. Phys. Anal. Geom. 12, 287-324 (2009). [TeX | PDF]
• The algebro-geometric initial value problem for the Ablowitz-Ladik hierarchy, with F. Gesztesy, H. Holden, and J. Michor, Discrete Contin. Dyn. Syst. 26:1, 151-196 (2010). [TeX | PDF]
• The Krein-von Neumann extension and its connection to an abstract buckling problem, with M. Ashbaugh, F. Gesztesy, M. Mitrea, and R. Shterenberg, Math. Nachr. 283:2, 165-179 (2010). [TeX | PDF]
• Isoprene and acetone concentration profiles during exercise on an ergometer, with J. King, A. Kupferthaler, K. Unterkofler, H. Koc, S. Teschl, G.T., W. Miekisch, J. Schubert, H. Hinterhuber, and A. Amann, J. Breath Res. 3, 027006, 16pp (2009). [DOC|PDF]
• Stability of the periodic Toda lattice in the soliton region, with H. Krüger, Int. Math. Res. Not. 2009:21 3996-4031 (2009). [TeX | PDF]
• Long-time asymptotics for the Camassa-Holm equation, with A. Boutet de Monvel, A. Kostenko, and D. Shepelsky, SIAM J. Math. Anal. 41:4, 1559-1588 (2009). [TeX | PDF]
• On the Cauchy problem for the Korteweg-de Vries equation with steplike finite-gap initial data I. Schwartz-type perturbations, with I. Egorova and K. Grunert, Nonlinearity 22, 1431-1457 (2009). [TeX | PDF]
• Relative oscillation theory for Jacobi matrices, with K. Ammann, 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. [TeX | PDF]
• Reconstruction of the transmission coefficient for steplike finite-gap backgrounds, with I. Egorova, Oper. Matrices 3, 205-214 (2009). [TeX | PDF]
• On the equivalence of different Lax pairs for the Kac-van Moerbeke hierarchy, with J. Michor, in Modern Analysis and Applications, V. Adamyan (ed.) et al., 445-453, Oper. Theory Adv. Appl. 191, Birkhäuser, Basel, 2009. [TeX | PDF]
• Long-time asymptotics of the Toda lattice for decaying initial data revisited, with H. Krüger, Rev. Math. Phys. 21:1, 61-109 (2009). [TeX | PDF]
• Long-time asymptotics for the Toda lattice in the soliton region, with H. Krüger, Math. Z. 262, 585-602 (2009). [TeX | PDF]
• Effective Prüfer angles and relative oscillation criteria, with H. Krüger, J. Differential Equations 245, 3823-3848 (2008). [TeX | PDF]
• On the absolutely continuous spectrum of Sturm-Liouville operators with applications to radial quantum trees, with M. Schmied and R. Sims, Oper. Matrices 2:3, 417-434 (2008). [TeX | PDF]
• Inverse scattering theory for one-dimensional Schrödinger operators with steplike finite-gap potentials, with A. Boutet de Monvel and I. Egorova, J. d'Analyse Math. 106:1, 271-316 (2008). [TeX | PDF]
• Local conservation laws and the Hamiltonian formalism for the Ablowitz-Ladik hierarchy, with F. Gesztesy, H. Holden, and J. Michor, Stud. Appl. Math. 120:4, 361-423 (2008). [TeX | PDF]
• Scattering theory for Jacobi operators with general steplike quasi-periodic background, with I. Egorova and J. Michor, Zh. Mat. Fiz. Anal. Geom. 4:1, 33-62 (2008). [TeX | PDF]
• Relative oscillation theory for Sturm-Liouville operators extended, with H. Krüger, J. Funct. Anal. 254:6, 1702-1720 (2008). [TeX | PDF]
• Relative oscillation theory, weighted zeros of the Wronskian, and the spectral shift function, with H. Krüger, Comm. Math. Phys. 287:2, 613-640 (2009). [TeX | PDF]
• The Ablowitz-Ladik hierarchy revisited, with F. Gesztesy, H. Holden, and J. Michor, in Methods of Spectral Analysis in Mathematical Physics, J. Janas (ed.) et al., 139-190, Oper. Theory Adv. Appl. 186, Birkhäuser, Basel, 2009. [TeX | PDF]
• Algebro-geometric finite-band solutions of the Ablowitz-Ladik hierarchy, with F. Gesztesy, H. Holden, and J. Michor, Int. Math. Res. Not. 2007, Art. ID rnm082, 55pp (2007). [TeX | PDF]
• Soliton solutions of the Toda hierarchy on quasi-periodic backgrounds revisited, with I. Egorova and J. Michor, Math. Nachr. 282:4, 526-539 (2009). [TeX | PDF]
• Scattering theory for Jacobi operators with steplike quasi-periodic background, with I. Egorova and J. Michor, Inverse Problems 23, 905-918 (2007). [TeX | PDF]
• On the approximation of isolated eigenvalues of ordinary differential operators, Proc. Amer. Math. Soc. 136, 2473-2476 (2008). [TeX | PDF]
• The algebro-geometric Toda hierarchy initial value problem for complex-valued initial data, with F. Gesztesy and H. Holden, Rev. Mat. Iberoamericana 24:1, 117-182 (2008). [TeX | PDF]
• Stability of periodic soliton equations under short range perturbations, with S. Kamvissis, Phys. Lett. A 364:6, 480-483 (2007). [TeX | PDF]
• Algebro-geometric constraints on solitons with respect to quasi-periodic backgrounds, Bull. London Math. Soc. 39:4, 677-684 (2007). [TeX | PDF]
• Inverse scattering transform for the Toda hierarchy with quasi-periodic background, with I. Egorova and J. Michor, Proc. Amer. Math. Soc. 135, 1817-1827 (2007). [TeX | PDF]
• Bound states of discrete Schrödinger operators with super-critical inverse square potentials, with D. Damanik, Proc. Amer. Math. Soc. 135, 1123-1127 (2007). [TeX | PDF]
• Trace formulas for Jacobi operators in connection with scattering theory for quasi-periodic background, with J. Michor, in Operator Theory, Analysis and Mathematical Physics, J. Janas (ed.) et al., 69-76, Oper. Theory Adv. Appl. 174, Birkhäuser, Basel, 2007. [TeX | PDF]
• Scattering theory for Jacobi operators with quasi-periodic background, with I. Egorova and J. Michor, Comm. Math. Phys. 264:3, 811-842 (2006). [TeX | PDF]
• On classical solutions of the relativistic Vlasov-Klein-Gordon system, with M. Kunzinger, G. Rein, and R. Steinbauer, Electron. J. Differential Equations 2005, No. 01, 1-17 (2005). [TeX | PDF]
• Reconstructing Jacobi matrices from three spectra, with J. Michor, in Spectral Methods for Operators of Mathematical Physics, J. Janas (ed.) et al., 151-154, Oper. Theory Adv. Appl. 154, Birkhäuser, Basel, 2004. [TeX | PDF]
• On the finiteness of the number of eigenvalues of Jacobi operators below the essential spectrum, with F. Luef., J. Difference Equ. Appl. 10, no. 3, 299-307 (2004). [TeX | PDF]
• Global weak solutions of the relativistic Vlasov-Klein-Gordon system, with M. Kunzinger, G. Rein, and R. Steinbauer, Comm. Math. Phys. 238, 367-378 (2003). [TeX | PDF]
• On the initial value problem of the Toda and Kac-van Moerbeke hierarchies, in Differential Equations and Mathematical Physics, R. Weikard and G. Weinstein (eds.), 375-384, AMS/IP Studies in Advanced Mathematics 16, Amer. Math. Soc., Providence, 2000. [TeX | PDF]
• On the Toda and Kac-van Moerbeke hierarchies, Math. Z. 231, 325-344 (1999). [TeX | PDF]
• Trace formulas and inverse spectral theory for Jacobi operators, Comm. Math. Phys. 196, no. 1, 175-202 (1998). [TeX | PDF]
• Inverse scattering transform for the Toda hierarchy, Math. Nachr. 202, 163-171 (1999). [TeX | PDF]
• Spectral deformations of Jacobi operators, J. Reine und Angew. Math. 491, 1-15 (1997). [TeX | PDF]
• Deforming the point spectra of one-dimensional Dirac operators, Proc. Amer. Math. Soc. 126, 2873-2881 (1998). [TeX | PDF]
• Renormalized oscillation theory for Dirac operators, Proc. Amer. Math. Soc. 126, 1685-1695 (1998). [TeX | PDF]
• Algebro-geometric quasi-periodic finite-gap solutions of the Toda and Kac-van Moerbeke hierarchies, with W. Bulla, F. Gesztesy, and H. Holden, Memoirs of the Amer. Math. Soc. 135/641, 1998. [TeX | PDF]
• Spectral deformations of one-dimensional Schrödinger operators, with F. Gesztesy and B. Simon, J. d'Analyse Math. 70, 267-324 (1996). [TeX | PDF]
• On isospectral sets of Jacobi operators, with F. Gesztesy and K. Maddaly, Com. Math. Phys. 181, 631-645 (1996). [TeX | PDF]
• Oscillation theory and renormalized oscillation theory for Jacobi operators, J. Differential Equations 129, 532-558 (1996). [TeX | PDF]
• Zeros of the Wronskian and renormalized oscillation theory, with F. Gesztesy and B. Simon, Am. J. Math. 118, 571-594 (1996). [TeX | PDF]
• The KdV hierarchy and associated trace formulas, with F. Gesztesy and R. Ratnaseelan, in Recent Developments in Operator Theory and its Applications, I. Gohberg (ed.) et al., 125-163, Oper. Theory Adv. Appl. 87, Birkhäuser, Basel, 1996. [TeX | PDF]
• Commutation methods for Jacobi operators, with F. Gesztesy, J. Differential Equations 128, 252-299 (1996). [TeX | PDF]
• On the double commutation method, with F. Gesztesy, Proc. Amer. Math. Soc. 124, 1831-1840 (1996). [TeX | PDF]

• Physiological modeling for analysis of exhaled breath, with J. King, H. Koc, K. Unterkofler, G.T., S. Teschl, P. Mochalski, H. Hinterhuber, and A. Amann, in "Volatile Biomarkers - Non-Invasive Diagnosis in Physiology and Medicine", A. Amann and D. Smith (eds), Elsevier 2013. [PDF]
• Spectral theory as influenced by Fritz Gesztesy, with K. Unterkofler, in "Spectral Analysis, Differential Equations and Mathematical Physics", H. Holden et al. (eds), 343-364, Proceedings of Symposia in Pure Mathematics 87, Amer. Math. Soc., Providence, 2013. [TeX | PDF]
• 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, with M.S. Ashbaugh, F. Gesztesy, M. Mitrea, and R. Shterenberg, in "Mathematical Physics, Spectral Theory and Stochastic Analysis", M. Demuth and W. Kirsch (eds.), 1-106, Oper. Theory Adv. Appl. 232, Birkhäuser, Basel, 2013. [TeX | PDF]
• Volatile organic compounds in exhaled breath: real-time measurements, modeling, and bio-monitoring applications, with J. King, K. Unterkofler, S. Teschl, A. Amann, and G.T., in "The 1st International Workshop on Innovative Simulation for Health Care", W. Backfrieder et al. (eds), 139-144, DIME University of Genova, 2012. [PDF]
• The role of mathematical modeling in VOC analysis using isoprene as a prototypic example, with H. Koc, J. King, G.T., K. Unterkofler, S. Teschl, P. Mochalski, H. Hinterhuber, and A. Amann, J. Breath Res. 5, 037102, 9pp (2011). [TeX | PDF]
• Almost everything you always wanted to know about the Toda equation, Jahresber. Deutsch. Math.-Verein. 103, no. 4, 149-162 (2001). [TeX | PDF]

• Soliton Equations and Their Algebro-Geometric Solutions. Volume II: (1+1)-Dimensional Discrete Models, with F. Gesztesy, H. Holden, and J. Michor, Cambridge Studies in Advanced Mathematics 114, Cambridge University Press, Cambridge, 2008. (ISBN: 978-0-521-75308-1)
• Jacobi Operators and Completely Integrable Nonlinear Lattices, Mathematical Surveys and Monographs 72, Amer. Math. Soc., Providence, 2000. (ISBN: 0-8218-1940-2) [PDF]

• Mathematik für Informatiker, Band 1: Diskrete Mathematik und Lineare Algebra, with S. Teschl,
  1rst ed. Springer Verlag, Berlin, 2006. (ISBN: 3-540-25782-9)
  2nd ed. Springer Verlag, Berlin, 2007. (ISBN: 978-3-540-70824-7)
  3rd ed. Springer Verlag, Berlin, 2008. (ISBN: 978-3-540-77431-0)
• Mathematik für Informatiker, Band 2: Analysis und Statistik, with S. Teschl,
  1rst ed. Springer Verlag, Berlin, 2006. (ISBN: 3-540-28064-2)
  2nd ed. Springer Verlag, Berlin, 2007. (ISBN: 978-3-540-72451-3)
  3rd ed. Springer Verlag, Berlin, (to appear).
• Mathematical Methods in Quantum Mechanics; With Applications to Schrödinger Operators,
  Graduate Studies in Mathematics 99, Amer. Math. Soc., Providence, 2009. (ISBN: 978-0-8218-4660-5)
• Ordinary Differential Equations and Dynamical Systems,
  Graduate Studies in Mathematics 140, Amer. Math. Soc., Providence, 2012. (ISBN: 978-0-8218-8328-0)
  A Chinese translation has been published by China Machine Press, Beijing. (ISBN: 978-7-111-33305-0)

• Spectral Analysis, Differential Equations and Mathematical Physics: A Festschrift in Honor of Fritz Gesztesy's 60th Birthday, Editors: H. Holden, B. Simon, and G. Teschl, Proceedings of Symposia in Pure Mathematics 87, Amer. Math. Soc., Providence, 2013. [PDF]

• Topics in Real and Functional Analysis, 218pp, (lecture notes). [PDF]
• Nonlinear Functional Analysis, 62pp, (lecture notes). [PDF]
• Getting Started with Mathematica, (Mathematica notebook).
• Cryptography with Mathematica, (Mathematica notebook).

• Spectral Theory for Jacobi Operators, PhD Thesis, University of Missouri, 1995. [TeX | PDF]
• Schrödingeroperator mit einer auf einem Rotationsellipsoid konzentrierten Wechselwirkung, Diploma Thesis, Technical University of Graz, 1993. [TeX | PDF]

• Mathematik in Wien; Universität Wien, with A. Cap, H.G. Feichtinger, H. Hauser, B. Lamel, and K. Sigmund, Internat. Math. Nachrichten 214, 17-47 (2010). [PDF]
• Biografie von Maria Hoffmann-Ostenhof, in "Wissenschafterinnen in und aus Österreich" - www.biografiA.at (to appear). [PDF]
• Mathematische Modellierung in der Atemgasanalyse, with J. King, K. Unterkofler, A. Amann, S. Teschl, and G.T., Schriftenreihe zur Didaktik der Mathematik der ÖMG 46, 1-7 (2013). [PDF]