Currently I am working within the FWF START project "Spectral Analysis and Applications to Soliton Equations" of Gerald Teschl at the faculty of mathematics of the University of Vienna. On this page you may find my publications, recent preprints (also available on arXiv) as well as a curriculum vitae.

Preprints

• An inverse spectral problem for a star graph of Krein strings, ... — PDF
• A coupling problem for entire functions and its application to the long-time asymptotics of integrable wave equations, with G. Teschl, ... — PDF
• Inverse uniqueness results for one-dimensional weighted Dirac operators, with A. Kostenko and G. Teschl, ... — PDF
• Singular Weyl–Titchmarsh–Kodaira theory for one-dimensional Dirac operators, with R. Brunnhuber, A. Kostenko and G. Teschl, ... — PDF
• Supersymmetry and Schrödinger-type operators with distributional matrix-valued potentials, with F. Gesztesy, R. Nichols and G. Teschl, ... — PDF

Publications

• An isospectral problem for global conservative multi-peakon solutions of the Camassa–Holm equation, with A. Kostenko, Comm. Math. Phys. (to appear)
• Inverse spectral theory for Sturm–Liouville operators with distributional potentials, with F. Gesztesy, R. Nichols and G. Teschl, J. Lond. Math. Soc. (2) (to appear) — PDF
• Weyl–Titchmarsh theory for Sturm–Liouville operators with distributional potentials, with F. Gesztesy, R. Nichols and G. Teschl, Opuscula Math. 33 (2013), no. 3, 467–563 — PDF
• On the isospectral problem of the dispersionless Camassa–Holm equation, with G. Teschl, Adv. Math. 235 (2013), 469–495 — PDF
• Singular Weyl–Titchmarsh–Kodaira theory for Jacobi operators, with G. Teschl, Oper. Matrices (to appear) — PDF
• Two inverse spectral problems for a class of singular Krein strings, Int. Math. Res. Not. (to appear) — PDF
• Direct and inverse spectral theory of singular left-definite Sturm–Liouville operators, J. Differential Equations 253 (2012), no. 2, 604–634 — PDF
  » Extended version with more detailed proofs — PDF
• Uniqueness results for one-dimensional Schrödinger operators with purely discrete spectra, with G. Teschl, Trans. Amer. Math. Soc. 365 (2013), no. 7, 3923–3942 — PDF
• Sturm–Liouville operators on time scales, with G. Teschl, J. Difference Equ. Appl. 18 (2012), no. 11, 1875–1887 — PDF
• Inverse uniqueness results for Schrödinger operators using de Branges theory, Complex Anal. Oper. Theory (to appear) — PDF
• Sturm–Liouville operators with measure-valued coefficients, with G. Teschl, J. Anal. Math. (to appear) — PDF
• On the connection between the Hilger and Radon–Nikodym derivatives, with G. Teschl, J. Math. Anal. Appl. 385 (2012), no. 2, 1184–1189 — PDF

Theses

• On the isospectral problem of the Camassa–Holm equation, doctoral thesis, University of Vienna, 2011 — PDF
• Direkte und inverse Spektraltheorie von Sturm–Liouville Differentialoperatoren, diploma thesis (in german), Vienna University of Technology, 2009 — PDF

Contact Information

Jonathan Eckhardt Faculty of mathematics University of Vienna Nordbergstrasse 15 1090 Vienna Austria Email: jonathan.eckhardt@univie.ac.at

Last modified: 2013-05-21