Publications

An abstract for each publication is available by selecting the corresponding link. All documents are available as TeX, DVI, 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, PostScript files with GhostScript from http://www.cs.wisc.edu/~ghost/, 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 files are also available from mp-arc and some from arxiv (front|author id). However, note that the files below are updated whenever I encounter a typo. You can also search MathSciNet, ZMATH, or Google Scholar. A list of coauthors is available as well.

• On the Cauchy problem for the Korteweg-de Vries equation with steplike finite-gap initial data II. Perturbations with finite moments, with I. Egorova [TeX | DVI | PDF]
• Unique continuation for discrete nonlinear wave equations, with H. Krüger [TeX | DVI | PDF]
• Stability of the periodic Toda lattice: Higher order asymptotics, with S. Kamvissis [TeX | DVI | PDF]
• Stability of the periodic Toda lattice under short range perturbations, with S. Kamvissis [TeX | DVI | 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), Contemp. Math., Amer. Math. Soc., Providence (to appear). [TeX | DVI | PDF]
• On the spatial asymptotics of solutions of the Toda lattice, Discrete Contin. Dyn. Syst. (to appear). [TeX | DVI | PDF]
• A Paley-Wiener theorem for periodic scattering with applications to the Korteweg-de Vries equation, with I. Egorova, Zh. Mat. Fiz. Anal. Geom. (to appear). [TeX | DVI | 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 | DVI | PDF]
• Trace formulas for Schrödinger operators in connection with scattering theory for finite-gap backgrounds, with A. Mikikits-Leitner, in Proceedings of the conference Operator Theory, Analysis and Mathematical Physics - OTAMP 2008, J. Janas (ed) et al., (to appear). [TeX | DVI | 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 | DVI | 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 | DVI | 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 | DVI | 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 | DVI | PDF]
• Isoprene and acetone concentration profiles during exercise on an ergometer, with J. King, A. Kupferthaler, K. Unterkofler, H. Koc, S. Teschl, W. Miekisch, J. Schubert, H. Hinterhuber, and A. Amann, J. Breath Res. 3, 027006, 16pp (2009). [PDF]
• Stability of the periodic Toda lattice in the soliton region, with H. Krüger, Int. Math. Res. Not. 2009, Art. ID rnp077, 36pp (2009). [TeX | DVI | 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 | DVI | 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 | DVI | 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 | DVI | PDF]
• Reconstruction of the transmission coefficient for steplike finite-gap backgrounds, with I. Egorova, Oper. Matrices 3, 205-214 (2009). [TeX | DVI | 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 | DVI | 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 | DVI | PDF]
• Long-time asymptotics for the Toda lattice in the soliton region, with H. Krüger, Math. Z. 262, 585-602 (2009). [TeX | DVI | PDF]
• Effective Prüfer angles and relative oscillation criteria, with H. Krüger, J. Diff. Eq. 245, 3823-3848 (2008). [TeX | DVI | 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 | DVI | 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 | DVI | 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 | DVI | 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 | DVI | PDF]
• Relative oscillation theory for Sturm-Liouville operators extended, with H. Krüger, J. Funct. Anal. 254:6, 1702-1720 (2008). [TeX | DVI | PDF]
• Relative oscillation theory, weighted zeros of the Wronskian, and the spectral shift function, with H. Krüger, Commun. Math. Phys. 287:2, 613-640 (2009). [TeX | DVI | 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 | DVI | 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 | DVI | 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 | DVI | PDF]
• Scattering theory for Jacobi operators with steplike quasi-periodic background, with I. Egorova and J. Michor, Inverse Problems 23, 905-918 (2007). [TeX | DVI | PDF]
• On the approximation of isolated eigenvalues of ordinary differential operators, Proc. Amer. Math. Soc. 136, 2473-2476 (2008). [TeX | DVI | 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 | DVI | PDF]
• Stability of periodic soliton equations under short range perturbations, with S. Kamvissis, Phys. Lett. A 364:6, 480-483 (2007). [TeX | DVI | PDF]
• Algebro-geometric constraints on solitons with respect to quasi-periodic backgrounds, Bull. London Math. Soc. 39:4, 677-684 (2007). [TeX | DVI | 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 | DVI | 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 | DVI | 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 | DVI | 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 | DVI | 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 | DVI | 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 | DVI | 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 | DVI | 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 | DVI | 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 | DVI | PDF]
• On the Toda and Kac-van Moerbeke hierarchies, Math. Z. 231, 325-344 (1999). [TeX | DVI | PDF]
• Trace formulas and inverse spectral theory for Jacobi operators, Comm. Math. Phys. 196, no. 1, 175-202 (1998). [TeX | DVI | PDF]
• Inverse scattering transform for the Toda hierarchy, Math. Nachr. 202, 163-171 (1999). [TeX | DVI | PDF]
• Spectral deformations of Jacobi operators, J. Reine und Angew. Math. 491, 1-15 (1997). [TeX | DVI | PDF]
• Deforming the point spectra of one-dimensional Dirac operators, Proc. Amer. Math. Soc. 126, 2873-2881 (1998). [TeX | DVI | PDF]
• Renormalized oscillation theory for Dirac operators, Proc. Amer. Math. Soc. 126, 1685-1695 (1998). [TeX | DVI | PDF]
• Spectral deformations of one-dimensional Schrödinger operators, with F. Gesztesy and B. Simon, J. d'Analyse Math. 70, 267-324 (1996). [TeX | DVI | PDF]
• On isospectral sets of Jacobi operators, with F. Gesztesy and K. Maddaly, Com. Math. Phys. 181, 631-645 (1996). [TeX | DVI | PDF]
• Oscillation theory and renormalized oscillation theory for Jacobi operators, J. Diff. Eq. 129, 532-558 (1996). [TeX | DVI | PDF]
• Zeros of the Wronskian and renormalized oscillation theory, with F. Gesztesy and B. Simon, Am. J. Math. 118, 571-594 (1996). [TeX | DVI | 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 | DVI | PDF]
• Commutation methods for Jacobi operators, with F. Gesztesy, J. Diff. Eq. 128, 252-299 (1996). [TeX | DVI | PDF]
• On the double commutation method, with F. Gesztesy, Proc. Amer. Math. Soc. 124, 1831-1840 (1996). [TeX | DVI | PDF]

• Almost everything you always wanted to know about the Toda equation, Jahresber. Deutsch. Math.-Verein. 103, no. 4, 149-162 (2001). [TeX | DVI | 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. (ISBN: 0-8218-0808-7) [TeX | DVI | PDF]
• Jacobi Operators and Completely Integrable Nonlinear Lattices, Mathematical Surveys and Monographs 72, Amer. Math. Soc., Providence, 2000. (ISBN: 0-8218-1940-2) [DVI | 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)

• 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)

• Functional Analysis, 137pp, (lecture notes). [DVI | PDF]
• Nonlinear Functional Analysis, 67pp, (lecture notes). [DVI | PDF]
• Ordinary Differential Equations and Dynamical Systems, 288pp, (lecture notes). [PS | PDF]
• Getting Started with Mathematica, (Mathematica notebook).
• Cryptography with Mathematica, (Mathematica notebook).

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