Manuscripts

• Publications

• Research projects

• CV 

• Geometric Analysis Seminar 

• ICMAM Latin America

• ICMAM for Central America and the Caribbean

Publications:

1. Cardona, D. L2-Maximal functions on graded Lie groups, to appear in IMRN (Int. Math. Res. Not.)  arXiv:2401.10830.

2. Cardona, D., Delgado, J., Ruzhansky, M.  Boundedness of the dyadic maximal function on graded Lie groups, to appear in Quart. J. Math.,  arXiv:2301.08964.

3. Cardona, D., Federico, S., Ruzhansky, M. Subelliptic sharp Gårding inequality on compact Lie groups., to appear in Pure Appl. Anal. arXiv:2110.00838

4. PhD Thesis: Cardona Sanchez, D. “Contributions to the theory of pseudo-differential operators : from compact to graded Lie groups,” Ghent University. Faculty of Sciences, Ghent, Belgium, 2023. 

5. Cardona D., Delgado J., Grajales, B., Ruzhansky M. Control of the Cauchy problem on Hilbert spaces: a global approach via symbol criteria, Commun. Pure Appl. Anal., Vol. 22(11), 3295-3329, (2023).   arXiv:2301.08999.

6. Cardona, D., Delgado, J., Ruzhansky, M.  A note on the local Weyl formula on compact Lie groups, to appear in J. Lie Theory, arXiv:2210.00311.

7. Cardona, D. Ruzhansky, M. Björk-Sjölin condition for strongly singular convolution operators on graded Lie groups,  Math. Z. 302, 1957–1981 (2022) arXiv:2205.03456

8. Cardona, D., Delgado, J., Ruzhansky, M. Drift diffusion equations with fractional diffusion on compact Lie groups.  J. Evol. Equ.  No. 22, Vol. 84, (2022).    arXiv:2205.02320

9. Cardona, D. Ruzhansky, M. Oscillating singular integral operators on compact Lie groups revisited.,  Math. Z. Vol. 303, 26 (2023)  arXiv:2202.10531

10. 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.

11. Book: Cardona, D. Grajales B, (Editors). Analysis and PDE in Latin America, ICMAM 2022 Latin America to appear in Research Perspectives: Ghent Analysis and PDE Center, Trends in Mathematics, Birkhäuser, 2024.  

12. Cardona, D. Delgado, J. Kumar, V. Ruzhansky, M. Lp-Lq-Boundedness of pseudo-differential operators on compact Lie groups, to appear in Osaka J. Math. , arXiv:2310.16247.

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

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

15. Cardona, D., Kumar, V., Ruzhansky, M., Tokmagambetov, N. Global Functional calculus, lower/upper bounds and evolution equations on manifolds with boundary, Adv. Oper. Theory, 8, 50 (2023). arXiv:2101.02519

16. Cardona, D., Delgado, J., Ruzhansky, M. Determinants and Plemelj-Smithies formulas,  Monatsh. Math., Vol. (199), 459–482, (2022).   arXiv:2012.13216

17. Book: Cardona, D. Restrepo, J. Ruzhansky, M (Editors). Extended Abstracts 2021/2022, Methusalem Lectures, Research Perspectives: Ghent Analysis and PDE Center, Trends in Mathematics, Birkhäuser, 2023.   

18. Memoir:  Cardona, D., Ruzhansky, M. Subelliptic pseudo-differential operators and Fourier integral operators on compact Lie groups, to appear in  MSJ Memoirs, Math. Soc.  Japan,   arXiv:2008.09651. 

19. 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

20. Cardona, D, Ruzhansky, M.  Littlewood-Paley theorem, Nikolskii inequality, Besov spaces, Fourier and spectral multipliers on graded Lie groups., to appear in Potential Analysis,   arXiv:1610.04701

21. 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. 

22. 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. 

23. 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 

24. Cardona, D. Ruzhansky, M.  Boundedness of pseudo-differential operators in subelliptic Sobolev and Besov spaces on compact Lie groups., to appear in Complex Var. Elliptic Equ.  arXiv:1901.06825

25. Cardona, D.  Ruzhansky, M. Hörmander condition for pseudo-multipliers associated to the harmonic oscillator,  to appear in Hokkaido Math. J.  arXiv:1810.01260

26.  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

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

28. 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. 

29. 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

30. 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

31. 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

32. 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

33.  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

34. 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. 

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

36. Cardona, D., Delgado, J., Ruzhansky, M.  Well-posedness for a class of pseudo-differential hyperbolic equations on the torus, accepted in Aequationes Math.

37. 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. 

38. Cardona, D. , E. Samuel  Barraza. Characterization of nuclear pseudo-multipliers associated to the harmonic oscillator.  UPB Sci. Bull. A: Appl. Math. Phys. Vol. 80 (4), 163-172, (2018).   arXiv:1803.00903

39. 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

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

41. 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).

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

43. 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

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

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

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

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

48. 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).

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

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

51. 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).

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

53.  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). 

54. 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).

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

56. 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

57. 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).

58. 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).

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

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

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

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

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

Chapters in Books:

64. Cardona, D. Kowacs, A. Global hypoellipticity on homogeneous vector bundles: necessary and sufficient conditions, to appear in Trends in Mathematics.

65. Cardona, D. Schatten-von Neumann classes Sp on the torus for 0 < p ≤ 2. In: Ruzhansky, M., Van Bockstal, K. (eds). Extended Abstracts 2021/2022. APDEGS 2021. Trends in Mathematics, vol 2. Birkhäuser, Cham. 

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

67. Cardona, D. The Index of Toeplitz Operators on Compact Lie Groups and on Simply Connected Closed 3-Manifolds. In: Kähler, U., Reissig, M., Sabadini, I., Vindas, J. (eds) Analysis, Applications, and Computations. ISAAC 2021. Trends in Mathematics. Birkhäuser, Cham.

68. 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

69. 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.
    
    

Preprints:

70. Cardona, D. Weighted boundedness for a class of local lacunary maximal operators, submitted. 

71. Cardona, D., Kirilov, A., de Moraes, W. A., Pedroso, Kowacz, A. On the Sobolev boundedness of vector fields on compact Riemannian manifolds, submitted, arXiv:2404.00182.

72. Cardona, D., Kumar, V., Ruzhansky, M. Pseudo-differential operators on homogeneous vector-bundles over compact homogeneous manifolds, submitted, arXiv:2403.08990.  

73. Cardona, D., Ruzhansky, M. The weak (1,1) boundedness of Fourier integral operators with complex phases, submitted, arXiv:2402.09054.  

74. Cardona, D. Estimates for the full maximal function on graded Lie groups, submitted, arXiv:2401.07086.

75. Cardona, D., Chatzakou, M., Delgado, J., Kumar, V., Ruzhansky, M.  Anharmonic semigroups and applications to global well-posedness of nonlinear heat equations, arXiv:2401.13750.  

76. Cardona, D. Kowacs, A. Global hypoellipticity of G-invariant operators on homogeneous vector-bundles, submitted, arXiv:2310.17288.

77. Cardona, D. Kumar, V. Ruzhansky, M. Lp-Lq-Boundedness of pseudo-differential operators on graded Lie groups, submitted, arXiv:2307.16094.

78. Cardona, D. Characterisation of  certain Schatten-von Neumann classes on the torus, submitted.

79. Cardona, D.,  Delgado,  J., Muñoz Tello, A. Gateaux differentiability of the Sobolev norm W(k,1)(M) on compact Riemannian manifolds, submitted.

80. Cardona D., Grajales, B., Ruzhansky M. On the sharpness of Strichartz estimates and spectrum of compact Lie groups, submitted, arXiv:2302.04139.

81. Cardona, D., Chatzakou, M., Ruzhansky, M., Toft, J.  Schatten-von Neumann properties for Hörmander classes on compact Lie groups, submitted, arXiv:2301.04044

82. Cardona, D., Chatzakou, M., Delgado, J., Ruzhansky, M.  Degenerate Schrödinger equations with irregular potentials, submitted,  arXiv:2302.02413.

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

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

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

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

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

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

89. 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 

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

91. 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  

92. 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