I am a current Ph.D. student at the Department of Mathematics: Analysis, Logic, and Discrete Mathematics, Ghent University.

The link to my homepage is here.

The list of my talks and outreach activities are here.

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The list of my publications (click here for an update list):

1. Cardona, D., Delgado, J., Ruzhansky, M. A note on the local Weyl formula on compact Lie groups, submitted, arXiv:2210.00311.

2. Cardona, D., Delgado, J., Ruzhansky, M. Estimates for sums of eigenfunctions of elliptic pseudo-differential operators on compact Lie groups, submitted, arXiv:2209.12092.

3. Cardona, D. Spectral inequalities for elliptic pseudo-differential operators on closed manifolds, submitted, arXiv:2209.10690.

4. Cardona, D., Duduchava, R., Hendricks, A., Ruzhansky, M. Global pseudo-differential operators on the Lie group G=(−1,1)ⁿ, submitted. arXiv:2209.09751.

5. Cardona, D. Ruzhansky, M. Björk-Sjölin condition for strongly singular convolution operators on graded Lie groups, Math. Z. arXiv:2205.03456

6. Cardona, D., Delgado, J., Ruzhansky, M. Drift diffusion equations with fractional diffusion on compact Lie groups., to appear in. J. Evol. Equ. arXiv:2205.02320

7. Cardona, D. Ruzhansky, M. Oscillating singular integral operators on compact Lie groups revisited. submitted. arXiv:2202.10531

8. Cardona, D. Ruzhansky, M. Boundedness of oscillating singular integrals on Lie groups of polynomial growth, submitted. arXiv:2201.12883

9. Cardona, D. Ruzhansky, M. Oscillating singular integral operators on graded Lie groups revisited, submitted. arXiv:2201.12881

10. Cardona, D., Delgado, J., Ruzhansky, M. Analytic functional calculus and Gårding inequality on graded Lie groups with applications to diffusion equations., to appear in J. Geom. Anal. submitted. arXiv:2111.07469

11. Cardona, D., Federico, S., Ruzhansky, M. Subelliptic sharp Gårding inequality on compact Lie groups., submitted. arXiv:2110.00838

12. Cardona, D., Ruzhansky, M. Sharpness of Seeger-Sogge-Stein orders for the weak (1,1) boundedness of Fourier integral operators., Vol. 119, 189–198 (2022). Arch. Math. arXiv:2104.09695.

13. Cardona, D., Delgado, J., Ruzhansky, M. Dixmier traces, Wodzicki residues, and determinants on compact Lie groups: the paradigm of the global quantisation. submitted. arXiv:2105.14949

14. Cardona, D., Ruzhansky, M. Fourier multipliers for Triebel-Lizorkin spaces on compact Lie groups., Collect. Math. Vol. 73, 477–504, (2022). arXiv:2101.12314

15. Cardona, D., Ruzhansky, M. Fourier multipliers for Triebel-Lizorkin spaces on graded Lie groups., submitted. arXiv:2101.05856.

16. Cardona, D., Esquivel, L. On the Benjamin Ono equation in the half line., Nonlinear Analysis. Vol. 212, (2021), Art. 112427. arXiv:2101.06992

17. Cardona, D., Kumar, V., Ruzhansky, M., Tokmagambetov, N. Expansion of traces and Dixmier traceability for global pseudo-differential operators on manifolds with boundary., submitted. arXiv:2101.05883

18. Cardona, D., Kumar, V., Ruzhansky, M., Tokmagambetov, N. Global Functional calculus, lower/upper bounds and evolution equations on manifolds with boundary., submitted. arXiv:2101.02519

19. Cardona, D., Delgado, J., Ruzhansky, M. Determinants and Plemelj-Smithies formulas, Monatsh. Math. arXiv:2012.13216

20. Cardona, D. On the multiplier problem for the ball on graded Lie groups., submitted. arXiv:2012.11057

21. Cardona, D., Ruzhansky, M. Subelliptic pseudo-differential operators and Fourier integral operators on compact Lie groups, submitted. arXiv:2008.09651.

22. Cardona, D., Delgado, J., Ruzhansky, M. Lp-bounds for pseudo-differential operators on graded Lie groups. J. Geom. Anal. Vol. 31, 11603-11647, (2021). arXiv:1911.03397

23. Cardona, D. The Wodzicki residue for pseudo-differential operators on compact Lie groups, to appear in Harmonic Analysis and Partial Differential Equations. Trends in Mathematics. arXiv:2201.12336

24. Cardona, D., Messiouene, R., Senoussaoui, A. Periodic Fourier integral operators in Lp spaces. C. R. Math. Acad. Sci. Paris. Vol. 359 (5), (2021), 547-553.

25. Cardona, D., Esquivel, L. Sharp Strichartz estimates for the Schrödinger equation on the sphere. J. Pseudo-Differ. Oper. Appl. Vol. 12, 23 (2021). arXiv:2006.08165.

26. Cardona, D., Kumar, V. The nuclear trace of vector-valued pseudo-differential operators with applications to Index theory., Math. Nachr. Vol. 294(9), 1657-1683, (2021). arXiv:1901.10010

27. Cardona, D., Kumar, V., Ruzhansky, M., Tokmagambetov, N. Lp–Lq boundedness of pseudo-differential operators on smooth manifolds and its applications to nonlinear equations., submitted. arXiv:2005.04936

28. Cardona, D. Ruzhansky, M. Boundedness of pseudo-differential operators in subelliptic Sobolev and Besov spaces on compact Lie groups., submitted. arXiv:1901.06825

29. Cardona, D. Ruzhansky, M. Hörmander condition for pseudo-multipliers associated to the harmonic oscillator, submitted. arXiv:1810.01260

30. Cardona, D. Sharp estimates for the Schrödinger equation associated to the twisted Laplacian. Rep. Math. Phys. Vol. 85(1), 29-39, (2020). arXiv:1810.02940

31. Cardona D. Lp-estimates for a Schrödinger equation associated with the harmonic oscillator. Electron. J. Differential Equations, Vol. (2019), No. 20, pp. 1-10. arXiv:1808.02906.

32. Cardona, D. The index of Toeplitz operators on compact Lie groups and simply connected closed 3-manifolds., to appear in, Analysis, Applications, and Computations– Selected contributions of the 13th ISAAC Congress, Ghent, Belgium, 2021.

33. Cardona, D., Kumar, V., Lp-boundedness and Lp-nuclearity of multilinear pseudo-differential operators on Zn and the torus Tn, J. Fourier Anal. Appl. Vol. 25 (6), 2973-3017, (2019). arXiv:1809.08380

34. Cardona, D. Messiouene, R., Senoussaoui, A. Lp-bounds for Fourier integral operators on the torus, to appear in Complex Var. Elliptic Equ. arXiv:1807.09892

35. Cardona, D. Pseudo-differential operators in Hölder spaces revisited. Weyl-Hörmander calculus and Ruzhansky-Turunen classes, Mediterr. J. Math. 16, no. 6. Art. 148, 17 pp. (2019). arXiv:1806.09245

36. Cardona, D., Kumar, V., Del Corral, C. Dixmier traces for discrete pseudo-differential operators. J. Pseudo-Differ. Oper. Appl. Vol. 11, 647–656, (2020). arXiv:1911.03924

37. Cardona, D. Besov continuity for global operators on compact Lie groups: the critical case p=q=∞, Trans. A. Razmadze Math. Inst Vol. 172 (3), , 354-360, (2018). arXiv:1807.00952

38. 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.

39. Cardona, D. The weak type (1,p) for convolution operators on locally compact groups, arXiv:1803.02413.

40. Cardona, D. Pseudo-differential operators on Zn with applications to discrete fractional integral operators. Bull. Iran. Math. Soc. 45 (4),1227–1241, (2019). arXiv:1803.00231.

41. 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), 163-172, (2018). arXiv:1803.00903

42. Cardona, D. Nuclear pseudo-differential operators in Besov spaces on compact Lie groups. J. Fourier Anal. Appl. Vol 23, (5), 1238-1262, (2017). arXiv:1610.09042

43. 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), (2019). arXiv:1703.07453

44. Cardona, D. On the boundedness of periodic pseudo-differential operators. Monatsh. Math. Vol. 185(2), 189-206, (2018). arXiv:1701.08184

45. Cardona, D., Del Corral, C. The Dixmier trace and the non-commutative residue for multipliers on compact manifolds. In: Georgiev V., Ozawa T., Ruzhansky M., Wirth J. (eds) Advances in Harmonic Analysis and Partial Differential Equations. Trends in Mathematics. Birkhäuser, Cham. https. arXiv:1703.07453.

46. Cardona, D. Besov continuity of pseudo-differential operators on compact Lie groups revisited. C. R. Math. Acad. Sci. Paris. Vol. 355, (5) , 533—537, (2017).

47. Cardona, D, Ruzhansky, M. Multipliers for Besov spaces on graded Lie groups. C. R. Math. Acad. Sci. Paris. Vol. 355, (4) , 400-405.(2017).

48. Cardona, D, Ruzhansky, M. Littlewood-Paley theorem, Nikolskii inequality, Besov spaces, Fourier and spectral multipliers on graded Lie groups., submitted. arXiv:1610.04701

49. Cardona, D. Besov continuity for pseudo-differential operators on compact homogeneous manifolds. J. Pseudo-Differ. Oper. Appl. Vol. 9, (4) , 861-880, (2018). arXiv:1607.00689

50. Cardona, D. Hölder-Besov boundedness for periodic pseudo-differential operators, J. Pseudo-Differ. Oper. Appl. Vol. 8, (1), 13–34 (2016). arXiv:1609.03514

51. Cardona, D. Besov continuity for Multipliers defined on compact Lie groups. Palest. J. Math. Vol. 5, (2), 35-44, (2016).

52. Cardona, D. On the singular values of the Fox-Li operator. J. Pseudo-Differ. Oper. Appl. Vol. 6, (4), 427-438, (2015).

53. Cardona, D. Invertibility for a class of Fourier multipliers. J. Pseudo-Differ. Oper. Appl. Vol. 6, (2), 215-225, (2015).

54. Cardona, D. Weak type (1,1) bounds for a class of periodic pseudo-differential operators. J. Pseudo-Differ. Oper. Appl. Vol. 5(4), 507-515, (2014).

55. Cardona, D. Hölder estimates for pseudo-differential operators on T¹. J. Pseudo-Differ. Oper. Appl. Vol. 5 (4), 517-525, (2014).

56. Cardona, D. L∞-BMO bounds for pseudo-multipliers associated with the harmonic oscillator. Rev. Colombiana Mat. Vol. 54(2), 93-108, (2020).

57. 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, (15), 739-750, (2017).

58. Cardona, D. A note on the Stein restriction conjecture and the restriction problem on the torus. E. J. Math. Anal. Appl. Vol. 8(2), 165-171, (2020).

59. Cardona, D., Kumar, V. Multilinear analysis for discrete and periodic pseudo-differential operators in Lp spaces, Rev. Integr. temas Mat. Vol 36(2), 151-164, (2018).

60. Cardona, D. On the nuclear trace of Fourier Integral Operators, Rev. Integr. temas Mat . Vol 37(2), 219-249, (2019). arXiv:1807.08389

61. 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), 49-57. (2018). arXiv:1803.07924

62. Cardona, D. Weak type (1,1) bounds for a class of operators with discrete kernel. Rev. Integr. Temas. Mat. Vol. 33 (1). 51-62.(2015).

63. Cardona, D., Del Corral, C. The Dixmier trace and the Wodzicki residue for pseudo-differential operators on compact manifolds, Rev. Integr. Temas. Mat. Vol. 38 (1), 67-79. (2020).

64. Cardona, D. A note on the Fourier transform in Hölder spaces. Rev. Elementos. Vol. 6(6), 61-66 (2016).

65. Cardona, D. Una nota sobre la transformada de Fourier en espacios de Hölder. Miscelánea Mat. No. 61, 11–20, (2015/16).

66. Cardona, D. Estimativos L2 para una clase de operadores pseudodiferenciales definidos en el toro. Rev. Integr. Temas Mat. Vol. 31, (2) 142-157, (2013).

67. Cardona, D. Invertibilidad de operadores pseudo-diferenciales definidos en Zn. Lect. Mat. Vol. 34 (2), 179-186, (2013)

68. Cardona, D. Operadores pseudodiferenciales definidos en medidas de Borel, Rev. Integr. Temas Mat. Vol. 31 (1) , 25-42, (2013).