Duván Cardona

I am a current Ph.D. student at the Department of Mathematics: Analysis, Logic, and de-2Discrete Mathematics, Ghent University.
I am working under the supervision of Professor Michael RuzhanskyI am interested in harmonic analysis, particularly in the theory of pseudo-differential operators and Fourier integral operators.  My work concerns mainly in the analysis of operators on Lie groups and its applications to PDE and spectral theory.
The link to my homepage is here.

The list of my publications:

  1. Cardona, D. Ruzhansky, M. Subelliptic pseudo-differential operators on compact Lie groups.
  2. Cardona, D. Delgado, J. Ruzhansky, M. Lp-bounds for pseudo-differential operators on graded Lie groups.
  3. Cardona, D. L∞-BMO bounds for pseudo-multipliers associated to the harmonic oscillator, submitted. arXiv:1905.03644
  4. Cardona, D. Pseudo-differential operators in Hölder spaces revisited. Weyl-Hörmander calculus and Ruzhansky-Turunen classes, Mediterr. J. Math. To appear. arXiv:1806.09245
  5. Cardona, D. Ruzhansky, M. Boundedness of pseudo-differential operators in subelliptic Sobolev and Besov spaces on compact Lie groups., submitted. arXiv:1901.06825
  6. Cardona, D. A note on the Stein restriction conjecture and the restriction problem on the torus, submitted. arXiv:1812.10641
  7. Cardona, D. Ruzhansky, M. Hörmander condition for pseudo-multipliers associated to the harmonic oscillator, submitted. arXiv:1810.01260
  8. Cardona, D. Sharp estimates for the Schrödinger equation associated to the twisted Laplacian, Rep. Math. Phys. To appear. arXiv:1810.02940
  9. Cardona D. Lp-estimates for a Schrödinger equation associated with the harmonic oscillator. Electron. J. Differential Equations, Vol. 2019, No. 20, pp. 1-10.(open access) arXiv:1808.02906.
  10. Cardona, D. The index of Toeplitz operators on compact Lie groups and simply connected closed 3-manifolds, submitted. arXiv:1809.10401.
  11. Cardona, D., Kumar, V., Lp-boundedness and Lp-nuclearity of multilinear pseudo-differential operators on Zn and the torus Tn, J. Fourier Anal. Appl. DOI: 10.1007/s00041-019-09689-7, arXiv:1809.08380
  12. Cardona, D. Messiouene, R., Senoussaoui, A. Lp-bounds for Fourier integral operators on the torus, Math. Nachr., to appear, arXiv:1807.09892
  13. Cardona, D., Kumar, V. Multilinear analysis for discrete and periodic pseudo-differential operators in Lp spaces , Rev. Integr. temas Mat. Vol 36, (2) (2018), 151-164. (open access)
  14. Cardona, D. On the nuclear trace of Fourier Integral Operators, Rev. Integr. temas Mat . Vol 37, (2) (2019), 219-249. arXiv:1807.08389
  15. Cardona, D. Kumar, V. Del Corral, C. Dixmier traces for discrete pseudo-differential operators, submitted.
  16. Cardona, D. Kumar, V. The nuclear trace of vector-valued pseudo-differential operators with applications to Index theory., submitted. arXiv:1901.10010
  17. Cardona, D. Besov continuity for global operators on compact Lie groups: the critical case p=q=∞, Trans. A. Razmadze Math. Inst (open access), Vol. 172, (3) (2018), 354-360 arXiv:1807.00952
  18. Cardona, D. On the index of pseudo-differential operators on compact Lie groups. J. Pseudo-Differ. Oper. Appl. Vol. 10 (2), 285-305 (2019), arXiv:1805.10404.
  19. D. Cardona, A brief description of operators associated to the quantum harmonic oscillator on Schatten-von Neumann classes. Rev. Integr. Temas Mat. Vol 36, 1 (2018), 49-57. (open access) arXiv:1803.07924
  20. Cardona, D. The weak type (1,p) for convolution operators on locally compact groups, arXiv:1803.02413.
  21. Cardona, D. Pseudo-differential operators on Zn with applications to discrete fractional integral operators. Bull. Iran. Math. Soc. To appear. DOI: 10.1007/s41980-018-00195-y. arXiv:1803.00231.
  22. Cardona, D. , E. Samuel Barraza. Characterization of nuclear pseudo-multipliers associated to the harmonic oscillator. UPB, Scientific Bulletin, Series A: Applied Mathematics and Physics. Vol. 80 (4), (2018), 163-172. (open access) arXiv:1803.00903
  23. Cardona, D. Nuclear pseudo-differential operators in Besov spaces on compact Lie groups. J. Fourier Anal. Appl. Vol 23, (5) (2017), 1238-1262. Vol 23, 5 (2017), 1238-1262.
  24. Barraza, E. Samuel., Cardona, D. On nuclear Lp multipliers associated to the harmonic oscillator, in:Springer Proceedings in Mathematics & Statistics, Springer, Imperial College London, UK, 2016. M. Ruzhansky and J. Delgado (Eds), DOI: 10.1007/978-3-030-05657-5_4 (2019). (see version in arxiv)
  25. Cardona, D. On the boundedness of periodic pseudo-differential operators. Monatsh. Math. Vol. 185, (2) (2018), 189-206. arXiv:1701.08184
  26. Cardona, D., Del Corral, C. The Dixmier trace and the Wodzicki residue for pseudo-differential operators on compact manifolds, submitted.
  27. Cardona, D., Del Corral, C. The Dixmier trace and the non-commutative residue for multipliers on compact manifolds, submitted. arXiv:1703.07453.
  28. Cardona, D. Besov continuity of pseudo-differential operators on compact Lie groups revisited. C. R. Math. Acad. Sci. Paris. Vol. 355, (5) (2017), 533—537.
  29. Cardona, D, Ruzhansky, M. Multipliers for Besov spaces on graded Lie groups. C. R. Math. Acad. Sci. Paris. Vol. 355, (4) (2017), 400-405. (open access).
  30. Cardona, D, Ruzhansky, M. ” Littlewood-Paley theorem, Nikolskii inequality, Besov spaces, Fourier and spectral multipliers on graded Lie groups”. submitted. arXiv:1610.04701
  31. Barraza, E. Samuel., Rivas, E., Cardona, D. A data structure to represent data sets with more than one order relation like polygons, Contemporary Engineering Sciences,Vol. 10, (2017), no. 15, 739 – 750,(open access)
  32. Cardona, D. Besov continuity for pseudo-differential operators on compact homogeneous manifolds. J. Pseudo-Differ. Oper. Appl. Vol. 9, (4) , (2018), 861-880.
  33. Cardona, D. Hölder-Besov boundedness for periodic pseudo-differential operators, J. Pseudo-Differ. Oper. Appl. Vol. 8, (1) (2016), 13–34.
  34. Cardona, D. Besov continuity for Multipliers defined on compact Lie groups. Palest. J. Math. Vol. 5, (2) (2016), 35-44. (open access)
  35. Cardona, D. On the singular values of the Fox-Li operator. J. Pseudo-Differ. Oper. Appl. Vol. 6, (4) (2015), 427-438.
  36. Cardona, D. A note on the Fourier transform in Hölder spaces. Rev. Elementos. Vol. 6, (6) (2016), 61-66.
  37. Cardona, D. Invertibility for a class of Fourier multipliers. J. Pseudo-Differ. Oper. Appl. Vol. 6, (2) (2015), 215-225.
  38. Cardona, D. Weak type (1,1) bounds for a class of operators with discrete kernel. Rev. Integr. Temas. Mat. Vol. 33 (1) (2015). 51-62.(open access)
  39. Cardona, D. Weak type (1,1) bounds for a class of periodic pseudo-differential operators. J. Pseudo-Differ. Oper. Appl.Vol. 5 (4) (2014), 507-515.
  40. Cardona, D. Hölder estimates for pseudo-differential operators on T^1 . J. Pseudo-Differ. Oper. Appl.Vol. 5 (4) (2014), 517-525.
  41. Cardona, D. Estimativos L2 para una clase de operadores pseudodiferenciales definidos en el toro. Rev. Integr. Temas Mat. Vol. 31, (2) (2013). 142-157.
  42. Cardona, D. Invertibilidad de operadores pseudo-diferenciales definidos en Zn Lect. Mat.Vol. 34 (2), 179-186 (2013)
  43. Cardona, D. Operadores pseudodiferenciales definidos en medidas de Borel, Rev. Integr. Temas Mat. Vol. 31 (1) (2013), 25-42.