I am a Senior Lecturer at Loughborough University and a postdoctoral researcher at the University of Vienna funded by the Austrian Science Fund (FWF).
On this page you may find my publications as well as a curriculum vitae.
Publications
 Trace formulas and continuous dependence of spectra for the periodic conservative Camassa–Holm flow, with A. Kostenko and N. Nicolussi, ... — PDF
 On the absolutely continuous spectrum of generalized indefinite strings II, with A. Kostenko and T. Kukuljan, ... — PDF
 On the absolutely continuous spectrum of generalized indefinite strings, with A. Kostenko, ... — PDF
 The inverse spectral problem for periodic conservative multipeakon solutions of the Camassa–Holm equation, with A. Kostenko, Int. Math. Res. Not. (to appear) — PDF
 The classical moment problem and generalized indefinite strings, with A. Kostenko, Integral Equations Operator Theory 90 (2018), no. 2, Art. 23, 30 pp — PDF
 Unique solvability of a coupling problem for entire functions, Constr. Approx. 49 (2019), no. 1, 123–148 — PDF
 A Lagrangian view on complete integrability of the twocomponent Camassa–Holm system, with K. Grunert, J. Integrable Syst. 2 (2017), no. 1, xyx002, 14 pp — PDF
 Realvalued algebrogeometric solutions of the twocomponent Camassa–Holm hierarchy, with F. Gesztesy, H. Holden, A. Kostenko and G. Teschl, Ann. Inst. Fourier (Grenoble) 67 (2017), no. 3, 1185–1230 — PDF
 The inverse spectral transform for the conservative Camassa–Holm flow with decaying initial data, Arch. Ration. Mech. Anal. 224 (2017), no. 1, 21–52 — PDF
 Spectral asymptotics for canonical systems, with A. Kostenko and G. Teschl, J. Reine Angew. Math. 736 (2018), 285–315 — PDF
 On spectral deformations and singular Weyl functions for onedimensional Dirac operators, with A. Beigl, A. Kostenko and G. Teschl, J. Math. Phys. 56 (2015), no. 1, 012102, 11 pp — PDF
 The inverse spectral problem for indefinite strings, with A. Kostenko, Invent. Math. 204 (2016), no. 3, 939–977 — PDF
 Quadratic operator pencils associated with the conservative Camassa–Holm flow, with A. Kostenko, Bull. Soc. Math. France 145 (2017), no. 1, 47–95 — PDF
 Inverse spectral problems for Schrödingertype operators with distributional matrixvalued potentials, with F. Gesztesy, R. Nichols, A. L. Sakhnovich and G. Teschl, Differential Integral Equations 28 (2015), no. 56, 505–522 — PDF
 Onedimensional Schrödinger operators with δ'interactions on Cantortype sets, with A. Kostenko, M. Malamud and G. Teschl, J. Differential Equations 257 (2014), no. 2, 415–449 — PDF
 An inverse spectral problem for a star graph of Krein strings, J. Reine Angew. Math. 715 (2016), 189–206 — PDF
 A coupling problem for entire functions and its application to the longtime asymptotics of integrable wave equations, with G. Teschl, Nonlinearity 29 (2016), no. 3, 1036–1046 — PDF
 Inverse uniqueness results for onedimensional weighted Dirac operators, with A. Kostenko and G. Teschl, in Spectral theory and differential equations, 117–133, Amer. Math. Soc. Transl. Ser. 2, 233, Amer. Math. Soc., Providence, RI, 2014 — PDF
 Singular Weyl–Titchmarsh–Kodaira theory for onedimensional Dirac operators, with R. Brunnhuber, A. Kostenko and G. Teschl, Monatsh. Math. 174 (2014), no. 4, 515–547 — PDF
 An isospectral problem for global conservative multipeakon solutions of the Camassa–Holm equation, with A. Kostenko, Comm. Math. Phys. 329 (2014), no. 3, 893–918 — PDF
 Inverse spectral theory for Sturm–Liouville operators with distributional potentials, with F. Gesztesy, R. Nichols and G. Teschl, J. Lond. Math. Soc. (2) 88 (2013), no. 3, 801–828 — 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
 Supersymmetry and Schrödingertype operators with distributional matrixvalued potentials, with F. Gesztesy, R. Nichols and G. Teschl, J. Spectr. Theory 4 (2014), no. 4, 715–768 — 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 7 (2013), no. 3, 695–712 — PDF
 Two inverse spectral problems for a class of singular Krein strings, Int. Math. Res. Not. IMRN 2014, no. 13, 3692–3713 — PDF

Direct and inverse spectral theory of singular leftdefinite Sturm–Liouville operators,
J. Differential Equations 253 (2012), no. 2, 604–634
— PDF
» Extended version with more detailed proofs — PDF  Uniqueness results for onedimensional 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 8 (2014), no. 1, 37–50 — PDF
 Sturm–Liouville operators with measurevalued coefficients, with G. Teschl, J. Anal. Math. 120 (2013), no. 1, 151–224 — 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
Reviews
 The Camassa–Holm equation and the string density problem, with A. Kostenko and G. Teschl, Internat. Math. Nachrichten Nr. 233 (2016), 1–24 — 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 Department of Mathematical Sciences Loughborough University Epinal Way Loughborough LE11 3TU UK Office: Room SCH.1.20 Email: J.Eckhardt@lboro.ac.uk 
Jonathan Eckhardt Faculty of Mathematics University of Vienna OskarMorgensternPlatz 1 1090 Vienna Austria Office: Room 03.126 Email: jonathan.eckhardt@univie.ac.at 