Main Pictures Translations Other
Main Pictures Translations Other
Marius Beceanu

Publications

This is a list of my publications, last updated September 22nd, 2026:

  1. Dispersive estimates for Schrödinger's and wave equations on Riemannian manifolds, preprint, arXiv:2501.06957
  2. Decay estimates for Schrödinger's equation with magnetic potentials in three dimensions (with H. Kwon), preprint, arXiv:2411.11787
  3. The eigenvalue problem for the Laplacian via conformal mapping and the Gohberg-Sigal theory (with J. Hong, H. Kwon, M. Lim), preprint, arXiv:2112.11026
  4. Spectral multipliers III: endpoint bounds, intertwining operators, and twisted Hardy spaces (with M. Goldberg), preprint, arXiv:2308.12829
  5. A semilinear Schrödinger equation with random potential (with A. Soffer), preprint, arXiv:1903.03451
  6. Large global solutions for nonlinear Schrödinger equations III, energy-supercritical cases (with Q. Deng, A. Soffer, Y. Wu), preprint, arXiv:1901.07709
  7. Large initial data global well-posedness for a supercritical wave equation (with A. Soffer), preprint, arXiv:1602.08163
  8. The Schrödinger equation with potential in random motion (with A. Soffer), preprint, arXiv:1111.4584, accepted by Letters in Mathematical Physics
  9. Spectral multipliers II: elliptic and parabolic operators and Bochner-Riesz means (with M. Goldberg), Journal of Differential Equations, Vol. 453, Part 2, February 2026, 113836, doi:10.1016/j.jde.2025.113836
  10. Pluriharmonic solutions to Yang-Mills equations: a C*-algebras approach (with S. Munshi and R. Yang), Complex Anal Synerg 11, 24 (2025), doi:10.1007/s40627-025-00175-z
  11. Spectral multipliers and wave propagation for Hamiltonians with a scalar potential (with M. Goldberg), Journal of Functional Analysis (2024), Vol. 286, Issue 6, 110300, doi:10.1016/j.jfa.2023.110300
  12. A positivity criterion for the wave equation and global existence of large solutions (with A. Soffer), Int. Math. Res. Notices 20 (2023), pp. 17911-17952, doi:10.1093/imrn/rnad127
  13. Strichartz estimates for the Klein-Gordon equation in R^{3+1} (with G. Chen), Pure Appl. Anal. 4(4), pp. 767-809 (2022), doi:10.2140/paa.2022.4.767
  14. Large global solutions for nonlinear Schrödinger equations II, mass-supercritical, energy-subcritical cases (with Q. Deng, A. Soffer, Y. Wu), Communications in Mathematical Physics (2021) Vol. 382, pp. 173-237, doi:10.1007/s00220-021-03971-w
  15. Large global solutions for nonlinear Schrödinger equations I, mass-subcritical cases (with Q. Deng, A. Soffer, Y. Wu), Advances in Mathematics (2021), Vol. 391, 107973, doi:10.1016/j.aim.2021.107973
  16. Approximate analytical solutions to the heat and Stokes equations on the half-line obtained by Fokas’ transform (with M. Lachaab), Journal of Applied Mathematics and Physics (2021), Vol. 9, No. 4, doi:10.4236/jamp.2021.94055
  17. Structure formulas for wave operators (with W. Schlag), American Journal of Mathematics (2020) 142, No. 3, pp. 751-807, doi:10.1353/ajm.2020.0025
  18. Structure formulas for wave operators under a small scaling-invariant condition (with W. Schlag), J. Spectr. Theory 9 (2019), pp. 967-990, doi:10.4171/jst/268
  19. Large outgoing solutions to supercritical wave equations (with A. Soffer), Int. Math. Res. Notices 20 (2018), pp. 6201-6253, doi:10.1093/imrn/rnx050
  20. Decay estimates for the wave equation in two dimensions, Journal of Differential Equations (2016), Vol. 260, Issue 6, pp. 5378-5420, doi:10.1016/j.jde.2015.12.009
  21. Dispersive estimates in R^3 with threshold eigenstates and resonances, Analysis & PDE 9-4 (2016), pp. 813-858, doi:10.2140/apde.2016.9.813
  22. A centre-stable manifold for the energy-critical wave equation in R^3 in the symmetric setting, Journal of Hyperbolic Differential Equations (2014), Vol. 11, No. 3, pp. 437-476, doi:10.1142/S021989161450012X
  23. Strichartz estimates and maximal operators for the wave equation in R^3 (with M. Goldberg), Journal of Functional Analysis (2014) 266, Issue 3, pp. 147-151, doi:10.1016/j.jfa.2013.11.010
  24. Structure of wave operators for a scaling-critical class of potentials, American Journal of Mathematics (2014) 136, No. 2, pp. 255-308, doi:10.1353/ajm.2014.0011
  25. Potentiels variables et équations dispersives, Séminaire Laurent Schwartz --- EDP et applications (2012-2013), Exp. No. 19, 11 pp., doi:10.5802/slsedp.45
  26. The Schrödinger equation with potential in rough motion (with A. Soffer), Communications in Partial Differential Equations (2012), Vol. 37, Issue 6, pp. 969-1000, doi:10.1080/03605302.2012.668257
  27. Dispersive estimates for the Schrödinger equation with scaling-critical potential (with M. Goldberg), Communications in Mathematical Physics (2012), Vol. 314, Issue 2, pp. 471-481, doi:10.1007/s00220-012-1435-x
  28. A critical centre-stable manifold for Schrödinger's equation in three dimensions, Communications on Pure and Applied Mathematics (2012), Vol. 65, Issue 4, pp. 431-507, doi:10.1002/cpa.21387
  29. New estimates for a time-dependent Schrödinger equation, Duke Mathematical Journal (2011), Vol. 159, No. 3, pp. 417-477, doi:10.1215/00127094-1433394
  30. A centre-stable manifold for the focussing cubic NLS in R^{1+3}, Communications in Mathematical Physics (2008), Vol. 280, Issue 1, pp. 145-205, doi:10.1007/s00220-008-0427-3
  31. Local exact controllability of the diffusion equation in one dimension, Abstract and Applied Analysis (2003), Vol. 2003, No. 14, pp. 793-811, doi:10.1155/S1085337503303033

A conference proceedings volume for which I am listed as an editor: link
Nonlinear Dispersive Waves and Fluids, edited by S. Zheng, M. Beceanu, J. Bona, G. Chen, T. V. Phan, A. Soffer, Contemporary Mathematics, Volume 725, AMS Book Series 2019

Collaborators

Gong Chen
Qingquan Deng
Michael Goldberg
Jiho Hong
Hyun-Kyoung Kwon
Mohamed Lachaab
Mikyoung Lim
Sachin Munshi
Wilhelm Schlag
Avy Soffer
Yifei Wu
Rongwei Yang

Earlier work

My PhD thesis, written under the supervision of Professor Wilhelm Schlag
PDF file
Also see the 2008-2012 publications on the list above

The following is a paper submitted to SICON in 2005. It is the generalization of my UAIC undergraduate thesis to arbitrarily many dimensions. Here is a revised version from 2007 that takes into account the referees' remarks
PDF file

My Princeton undergraduate thesis, supervised by Professors Sergiu Klainerman and Igor Rodnianski
PDF file

My undergraduate thesis at UAIC Iași, supervised by Professor Viorel Barbu
English Romanian
Also see the 2003 publication on the list above

My two junior projects at Princeton
The first was done within the Junior Seminar, run by Professor Ramin Takloo-Bighash and Steve J. Miller. It investigates some elementary properties of the period of the continued fraction of √n
PDF file
The second was done under the supervision of Professor Peter Sarnak. It provides a computational confirmation of the Taniyama-Shimura conjecture, for non-integer primes in Z[i] of norm up to 45,000
PDF file

More

Papers on ArXiv: link

Google Scholar listing: link

ResearchGate profile: link