Preprints:

• The conservative Camassa-Holm flow with step-like irregular initial data, (with J. Eckhardt), submitted, arXiv:2310.06658.

Monograph:

• Laplacians on Infinite Graphs, (with N. Nicolussi), Memoirs Eur. Math. Soc. 3 (2023), 240pp.

Review Articles:

• Laplacians on infinite graphs: discrete vs. continuous, (with N. Nicolussi), 8th European Congress of Mathematics (Portoroz, 20-26 June, 2021), EMS Press, pp.295-232, 2023 (arXiv:2110.03566).
• The Camassa-Holm equation and the string density problem, (with J. Eckhardt and G. Teschl), Intern. Math. Nachr. 233, 1-24 (2016) (arXiv:1701.03598)
• 1-D Schrödinger operators with local point interactions: a review, (with M. Malamud), in "Spectral Analysis, Integrable Systems, and Ordinary Differential Equations", H. Holden et al. (eds), Proceedings of Symposia in Pure Mathematics 87, Amer. Math. Soc., (2013), 235-262 (arXiv:1303.4055)

Papers:

• Trace formulas and inverse spectral theory for generalized indefinite strings, (with J. Eckhardt), Invent. Math. 238, no. 2, 391-502 (2024); arXiv:2311.01189
• Generalized indefinite strings with purely discrete spectrum, (with J. Eckhardt), in: "From Complex Analysis to Operator Theory: A Panorama. In Memory of Sergey Naboko", M. Brown (ed.) et al., Oper. Theory Adv. Appl. 291, 435-474 (2023) (arXiv:2106.13138)
• On the absolutely continuous spectrum of generalized indefinite strings II, (with J. Eckhardt and T. Kukuljan), Israel J. Math. 250, 307-344 (2022) (arXiv:1906.05106)
• Self-adjoint and Markovian extensions of infinite quantum graphs, (with D. Mugnolo and N. Nicolussi), J. London Math. Soc. 105, no.2, 1262-1313 (2022) (arXiv:1911.04735)
• A Glazman-Povzner-Wienholtz Theorem on graphs, (with M. Malamud and N. Nicolussi), Adv. Math. 395, ID 108158 (2022) (arXiv:2105.09931)
• On the absolutely continuous spectrum of generalized indefinite strings, (with J. Eckhardt), Ann. Henri Poincaré 22, no.11, 3529-3564 (2021) (arXiv:1902.07898)
• A note on the Gaffney Laplacian on infinite metric graphs, (with N. Nicolussi), J. Funct. Anal. 280, no.10, Art: 109216 (2021) (arXiv:2108.08185)
• Quantum graphs on radially symmetric antitrees, (with N. Nicolussi), J. Spectral Theory 11, no.2, 411-460 (2021) (arXiv:1901.05404)
• Heat kernels of the discrete Laguerre operators, Lett. Math. Phys. 111, 2:32 (2021) (arXiv:2007.14963)
• The inverse spectral problem for periodic conservative multi-peakon solutions of the Camassa-Holm equation, (with J. Eckhardt), Int. Math. Res. Notices (IMRN), 2020, no. 16, 5126-5151 (2020) (arXiv:1801.04612)
• Trace formulas and continuous dependence of spectra for the periodic conservative Camassa-Holm flow, (with J. Eckhardt and N. Nicolussi), J. Differential Equations 268, no. 6, 3016-3034 (2020) (arXiv:1907.01911)
• Spectral estimates for infinite quantum graphs, (with N. Nicolussi), Calc. Var. Partial Differential Equations 58, no. 1, Art ID 15 (2019) (arXiv:1711.02428)
• Spectral theory of infinite quantum graphs, (with P. Exner, M. Malamud, and H. Neidhardt), Ann. Henri Poincaré 19, no. 11, 3457-3510 (2018) (arXiv:1705.01831)
• Jacobi polynomials, Bernstein-type inequalities and dispersion estimates for the discrete Laguerre operator, (with T. Koornwinder and G. Teschl), Adv. Math. 333, 796-821 (2018) (arXiv:1602.08626)
• On the Hamiltonian-Krein Index for a non-self-adjoint spectral problem, (with N. Nicolussi), Proc. Amer. Math. Soc. 146, no. 9, 3907-3921 (2018) (arXiv:1712.01702)
• Dispersion estimates for spherical Schrödinger equations with critical angular momentum, (with M. Holzleitner and G. Teschl), in "Partial Differential Equations, Mathematical Physics, and Stochastic Analysis", F. Gesztesy et al. (eds), EMS Congress Reports, pp. 319-348, 2018. (arXiv:1611.05210)
• The classical moment problem and generalized indefinite strings, (with J. Eckhardt), Integr. Equat. Oper. Theory 90, 2:23 (2018) (arXiv:1707.08394)
• Spectral asymptotics for canonical systems, (with J. Eckhardt and G. Teschl), J. reine angew. Math. 736, 285-315 (2018) (arXiv:1412.0277)
• Infinite quantum graphs, (with P. Exner, M. Malamud, and H. Neidhardt), Doklady Math. 95, no.1, 31-36 (2017)
• Real-valued algebro-geometric solutions of the two-component Camassa-Holm hierarchy, (with J. Eckhardt, F. Gesztesy, H. Holden, and G. Teschl), Ann. Inst. Fourier (Grenoble) 67, no.3, 1185-1230 (2017) (arXiv:1512.03956)
• Quadratic operator pencils associated with the conservative Camassa-Holm flow, (with J. Eckhardt), Bull. Soc. Math. France 145, no.1, 47-95 (2017) (arXiv:1406.3703)
• Dispersion estimates for spherical Schrödinger equations: The effect of boundary conditions, (with M. Holzleitner and G. Teschl), Opuscula Math. 36, 769-786 (2016) (arXiv:1601.01638)
• Dispersion estimates for the discrete Laguerre operator, (with G. Teschl), Lett. Math. Phys. 106, 545-555 (2016) (arXiv:1510.07019)
• Schrödinger operators with δ-interactions in a space of vector-valued functions, (with M. Malamud and D. Natiagailo), Math. Notes 100, no.1, 59-77 (2016) (arXiv:1603.00594)
• Dispersion estimates for spherical Schrödinger equations, (with G. Teschl and J. H. Toloza), Ann. Henri Poincaré 17, no.11, 3147-3176 (2016) (arXiv:1504.03015)
• The inverse spectral problem for indefinite strings, (with J. Eckhardt), Invent. Math. 204, no.3, 939-977 (2016) (arXiv:1409.0139)
• On spectral deformations and singular Weyl functions for one-dimensional Dirac operators, (with A. Beigl, J. Eckhardt and G. Teschl), J. Math. Phys. 56, Art ID 012102 (2015) (arXiv:1410.1152)
• A note on J-positive block operator matrices, Integr. Equat. Oper. Theory 81, 113-125 (2015) (arXiv:1403.2406)
• Schrödinger operators with δ'-interactions on a Cantor type set, (with J. Eckhardt, M. Malamud and G. Teschl), J. Differential Equations 257, 415–449 (2014) (arXiv:1401.7581)
• On a necessary aspect for the Riesz basis property for indefinite Sturm–Liouville problems, Math. Nachr. 287, no. 14-15, 1710-1732 (2014) (arXiv:1202.2444)
• Singular Weyl-Titchmarsh-Kodaira theory for one-dimensional Dirac operators, (with R. Brunnhuber, J. Eckhardt, and G. Teschl), Monatsh. Math. 174, 515-547 (2014). (arXiv:1305.3099)
• The Riesz basis property of an indefinite Sturm-Liouville problem with non-separated boundary conditions, (with B. Ćurgus and A. Fleige), Integr. Equat. Oper. Theory 77, 533–557 (2013) (arXiv:1306.1329)
• An isospectral problem for global conservative multi-peakon solutions of the Camassa-Holm equation, (with J. Eckhardt), Comm. Math. Phys. 239, 893–918 (2014) (arXiv:1406.3702)
• Spectral analysis of semibounded Schrödinger operators with δ'-interactions, (with M. Malamud), Ann. Henri Poincaré 15, 501-541 (2014) (arXiv:1212.1691)
• Spherical Schrödinger operators with δ-interactions, (with S. Albeverio, M. Malamud, and H. Neidhardt), J. Math. Phys. 54, Art ID: 052103 (2013), 24 pages. (arXiv:1211.4048)
• The similarity problem for indefinite Sturm–Liouville operators and the HELP inequality, Adv. Math. 246, 368–413 (2013) (arXiv:1207.2586)
• Spectral analysis of indefinite Sturm–Liouville operators, Funct. Anal. Appl. 48, no.3, 88-92 (2014).
• Spectral asymptotics for perturbed spherical Schrödinger operators and applications to quantum scattering, (with G. Teschl) Comm. Math. Phys. 322, 255-275 (2013) (arXiv:1205.5049)
• Weyl–Titchmarsh theory for Schrödinger operators with strongly singular potentials, (with A. Sakhnovich and G. Teschl), Int. Math. Res. Notices (IMRN), 2012, no. 8, 1699–1747 (2012) (arXiv:1007.0136)
• Commutation methods for Schrödinger operators with strongly singular potentials, (with A. Sakhnovich and G. Teschl), Math. Nachr. 285, no. 4, 392–410 (2012) (arXiv:1010.4902)
• On the singular Weyl–Titchmarsh function of perturbed spherical Schrödinger operators, (with G. Teschl), J. Differential Equations, 250, 3701–3739, (2011) (arXiv:1008.1526)
• The similarity problem for indefinite Sturm–Liouville operators with periodic coefficients, Oper. Matrices 5, no. 4, 707–722 (2011) (arXiv:1004.3991)
• Spectral theory of semi-bounded Sturm-Liouville operators with local interactions on a discrete set, (with S. Albeverio and M. Malamud), J. Math. Phys. 51, 102102, 24 pp. (2010)
• Inverse eigenvalue problems for perturbed spherical Schrödinger operators, (with A. Sakhnovich and G. Teschl), Inverse Problems 26, 105013, 14pp (2010) (arXiv:1004.4175)
• 1–D Schrödinger operators with local point interactions on a discrete set, (with M. Malamud), J. Differential Equations 249, 253–304 (2010) (arXiv:0908.3542)
• One dimensional Schrödinger operator with δ-interactions, (with M. Malamud), Funct. Anal. Appl. 44, no. 2, 151–155 (2010) (MathNet.ru)
• Schrödinger operators with δ'-interactions and the Krein-Stieltjes string, (with M. Malamud), Doklady Math. 81, no. 3, 342–347 (2010)
• Long-time asymptotics for the Camassa–Holm equation, (with A. Boutet de Monvel, D. Shepelsky, and G. Teschl), SIAM J. Math. Anal. 41, no. 4, 1559–1588 (2009) (arXiv:0902.0391)
• On similarity of J–nonnegative Sturm–Liouville operators to self–adjoint operators, (with I.M. Karabash), Funct. Anal. Appl. 43, no.1, 81–84 (2009) (MathNet.ru)
• The similarity problem for J-nonnegative Sturm-Liouville operators, (with I.M. Karabash and M.M. Malamud), J. Differential Equations 246, 964–997 (2009) (arXiv:0803.1496)
• Indefinite Sturm-Liouville operators with the singular critical point zero, (with I.M. Karabash), Proc. Roy. Soc. Edinburgh A, no.4, 801–820 (2008) (arXiv:0612137)
• Similarity of some J–nonnegative operators to self–adjoint operators, Math. Notes, 80, no. 1, 135–138 (2006) (MathNet.ru)
• A spectral analysis of some indefinite differential operators, Methods Funct. Anal. Topology, 12, no. 2, 157–169 (2006).
• The Krein string and characteristic functions of non-self-adjoint operators, Zapiski Nauchnih Seminarov POMI, 327 (2005), 115–134 (MathNet.ru)
• On similarity to a self–adjoint one of some indefinite Sturm–Liouville operators with singular potential, Math. Notes, 78, no. 1, 147–151 (2005) (MathNet.ru)
• Spectral analysis of non-self-adjoint operators type (sgnx) (D2 + aD + bI + cδ), Reports of the NAS of Ukraine, no. 8, 24–29 (2004)
• Similarity of (sgn x)(D2+cδ) type operators to normal and self–adjoint operators, (with I.M. Karabash), Math. Notes, 74, no. 1, 127–131 (2003) (MathNet.ru)
• On the instability index of quadratic self–adjoint operator pencils, Math. Notes 72, 285–290 (2002) (MathNet.ru)

Refereed Papers in Proceedings:

• Inverse uniqueness results for one-dimensional weighted Dirac operators, (with J. Eckhardt and G. Teschl, ), in "Spectral Theory and Differential Equations: V.A. Marchenko 90th Anniversary Collection", E. Khruslov, L. Pastur, and D. Shepelsky (eds), 117-133, Advances in the Mathematical Sciences 233, Amer. Math. Soc., Providence, 2014. arXiv:1305.3100
• Spectral analysis of differential operators with indefinite weights and a local point interaction, (with I.M. Karabash), Oper. Theory: Adv. and Appl. 175, 169–191 (2007).
• Spectral analysis of some indefinite Sturm–Liouville operators, Operator theory 20, 131–141, Theta Ser. Adv. Math., 6, Theta, Bucharest, 2006.