Duván Cardona

I am a FWO Research fellow at Ghent University funded by the Research Foundation Flanders FWO. I obtained my PhD in Mathematics in August 2023 under the supervision of Prof. Dr. Michael Ruzhansky. I am interested in harmonic analysis, particularly in the theory of pseudo-differential operators and Fourier integral operators.  My work is concerned mainly with the analysis of operators on Lie groups and its applications to PDE and spectral theory. 

  • The link to my Homepage is here.
  • The link to my Portfolio Site is here
  • You can explore the ICMAM Books here!  A  series of volumes related to the mathematical research at ICMAM Latin America and published by the Springer Series of the Ghent Analysis and PDE Center.
  • Link to my ResearchGate page here.
  • Link to my Google Scholar page here.
  • Link to my Zentralblatt MATH page here.
  • Link to my Semantic Scholar page here.
  • Link to my Publons page here.
  • Link to my arXiv page here.

Book/Memoir:

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

  1. Cardona, D., Martinez, M. A. Boundedness of pseudo-differential operators on the torus revisited, I.,
    J. Math. Anal. Appl., 554, Vol. 2, No. 129959, 2025. arXiv:2502.20575.
    Link

  2. Hurtado Quiceno, Andrea, V., Cardona, D. The constant in the Sobolev inequality and the boundedness of subelliptic operators on compact Lie groups, to appear in:
    Commun. Anal. Mech.
    Link

  3. Cardona, D., Chatzakou, M., Delgado, J., Kumar, V., Ruzhansky, M. Anharmonic semigroups and applications to global well-posedness of nonlinear heat equations, to appear in:
    J. Math. Phys., Vol. 66 (2025), paper no. 081509. arXiv:2401.13750.
    Link

  4. Cardona, D., Ruzhansky, M. Oscillating singular integral operators on graded Lie groups revisited, to appear in
    J. Lie Theory, arXiv:2201.12881.
    Link

  5. Cardona, D., Chatzakou, M., Delgado, J., Ruzhansky, M. Degenerate Schrödinger equations with irregular potentials, to appear in:
    Anal. Appl., arXiv:2302.02413.
    Link

  6. Cardona, D., Kirilov, A., de Moraes, W. A., Pedroso, Kowacz, A. On the Sobolev boundedness of vector fields on compact Riemannian manifolds,
    J. Pseudo-Differ. Oper. Appl. 16, 52 (2025). arXiv:2404.00182.
    Link

  7. Cardona, D., Kumar, V., Ruzhansky, M., Tokmagambetov, N. Lp-Lq boundedness of pseudo-differential operators on smooth manifolds and its applications to nonlinear equations,
    Ann. Funct. Anal., 6 (2025), no. 3, 50.  arXiv:2005.04936.
    Link

  8. Book: Cardona, D., Grajales, B. (Editors). Analysis and PDE in Latin America, ICMAM 2023-2024, Research Perspectives: Ghent Analysis and PDE Center,
    Trends in Mathematics, Birkhäuser, to appear.
    Link

  9. Cardona, D., Kumar, V., Ruzhansky, M. Lp-Lq-Boundedness of pseudo-differential operators on graded Lie groups,
    New York J. Math. 31 (2025), 722-748. arXiv:2307.16094.
    Link 

  10. Cardona, D., Kumar, V., Ruzhansky, M., Tokmagambetov, N. Expansion of traces and Dixmier traceability for global pseudo-differential operators on manifolds with boundary,
    Adv. Oper. Theory.  10 (2025), 10(53). arXiv:2101.05883.
    Link

  11. Cardona, D. L2-Maximal functions on graded Lie groups,
    IMRN (Int. Math. Res. Not.), Vol. 2024 (14), 10776-10789, (2024). arXiv:2401.10830.
    Link

  12. Cardona, D. Weighted boundedness for a class of local lacunary maximal operators,
    J. Math. Sci. 289, 926–943 (2025).
    Link

  13. Cardona, D., Delgado, J., Ruzhansky, M. Estimates for sums of eigenfunctions of elliptic pseudo-differential operators on compact Lie groups,
    J. Geom. Anal., Vol. 34, 374 (2024). arXiv:2209.12092.
    Link

  14. Cardona, D., Delgado, J., Ruzhansky, M. Boundedness of the dyadic maximal function on graded Lie groups,
    Quart. J. Math., Vol. 75(3), 809-834, (2024). arXiv:2301.08964.
    Link

  15. Cardona, D., Federico, S., Ruzhansky, M. Subelliptic sharp Gårding inequality on compact Lie groups,
    Pure Appl. Anal., Vol. 6, No. 2, 455–485, (2024). arXiv:2110.00838.
    Link

  16. Cardona, D., Chatzakou, M., Ruzhansky, M., Toft, J. Schatten-von Neumann properties for Hörmander classes on compact Lie groups, to appear in:
    Forum Math., arXiv:2301.04044.
    Link

  17. 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.
    Link

  18. 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.
    Link

  19. Cardona, D., Delgado, J., Ruzhansky, M. A note on the local Weyl formula on compact Lie groups,
    J. Lie Theory, 34(1), 237–248, (2024). arXiv:2210.00311.
    Link

  20. 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.
    Link

  21. 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.
    Link

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

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

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

  25. 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.
    Link

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

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

  28. 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.
    Link

  29. Cardona, D., Kowacs, A. Global hypoellipticity of G-invariant operators on homogeneous vector-bundles,
    J. Pseudo-Differ. Oper. Appl., Vol. 16, 23 (2025). arXiv:2310.17288.
    Link

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

  31. 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.
    Link

  32. 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.
    Link

  33. 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.
    Link

  34. Cardona, D., Ruzhansky, M. Littlewood-Paley theorem, Nikolskii inequality, Besov spaces, Fourier and spectral multipliers on graded Lie groups,
    Potential Analysis, Vol. 60, 965-1005, (2024). arXiv:1610.04701.
    Link

  35. 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.
    Link

  36. 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.
    Link

  37. 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.
    Link

  38. Cardona, D., Ruzhansky, M. Boundedness of pseudo-differential operators in subelliptic Sobolev and Besov spaces on compact Lie groups,
    Complex Var. Elliptic Equ., Vol. 69(7), 1049–1082, (2023). arXiv:1901.06825.
    Link

  39. Cardona, D., Ruzhansky, M. Hörmander condition for pseudo-multipliers associated to the harmonic oscillator,
    Hokkaido Math. J. Vol. 54, No. 1, (2025). arXiv:1810.01260.
    Link

  40. 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.
    Link

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

  42. 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.
    Link

  43. 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.
    Link

  44. Cardona, D., Messiouene, R., Senoussaoui, A. Lp-bounds for Fourier integral operators on the torus,
    Complex Var. Elliptic Equ., 69(2), 252-269, (2022). arXiv:1807.09892.
    Link

  45. 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.
    Link

  46. 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.
    Link

  47. 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.
    Link

  48. 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.
    Link

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

  50. Cardona, D., Delgado, J., Ruzhansky, M. Well-posedness for a class of pseudo-differential hyperbolic equations on the torus,
    Aequat. Math., Vol. 98, 1019–1038 (2024).
    Link

  51. 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.
    Link

  52. 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.
    Link

  53. 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.
    Link

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

  55. 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).
    Link

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

  57. 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.
    Link

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

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

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

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

  62. 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).
    Link

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

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

  65. 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).
    Link

  66. 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).
    Link

  67. 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).
    Link

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

  69. Cardona, D. 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.
    Link

  70. 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).
    Link

  71. 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).
    Link

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

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

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

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

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

    Chapters in Books

  77. Cardona, D., Martinez, M. A. Boundedness of pseudo-differential operators on the torus via kernel estimates, to appear in Trends in Mathematics.

  78. Cardona, D., Martinez, M. A. Boundedness of toroidal pseudo-differential operators on Hardy spaces, to appear in Trends in Mathematics.

  79. Cardona, D., Castro, T., Correa, S., De la Cruz, R., Mathematics and Memory: A Seminar of Analysis and Differential Equations for Latin America, to appear in: Trends in Mathematics.
    Link

  80. Cardona, D., Hurtado Quiceno, Andrea, V. Sobolev inequality and mapping properties of pseudo-differential operators on compact Lie groups, to appear in Trends in Mathematics.
    Link

  81. Cardona, D., Mapping properties of weighted Maximal Functions, to appear in Trends in Mathematics.
    Link

  82. Cardona, D., Boundedness of Fourier integral operators revisited, to appear in Trends in Mathematics.
    Link

  83. Cardona, D., Mapping Properties of Maximal Functions on Graded Lie Groups. In: Avetisyan, Z., Ruzhansky, M., Vagharshakyan, A. (eds)
    Analysis, PDEs, and Applications. GMG 2024. Trends in Mathematics., vol 13. Birkhäuser, Cham.
    Link

  84. Cardona, D., Duduchava, R., Hendrickx, A., Ruzhansky, M. Generic Bessel Potential Spaces on Lie Groups,
    Tbilisi Analysis and PDE Seminar. TAPDES 2023. Trends in Mathematics, Vol 7. Birkhäuser, Cham.
    Link

  85. Cardona, D., Kowacs, A. Global hypoellipticity on homogeneous vector bundles: necessary and sufficient conditions,
    Modern Problems in PDEs and Applications. MWCAPDE 2023. Trends in Mathematics, Vol 4. Birkhäuser, Cham.
    Link

  86. 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.
    Link

  87. Cardona, D. The Wodzicki residue for pseudo-differential operators on compact Lie groups, In: Ruzhansky, M., Wirth, J. (eds).
    Harmonic Analysis and Partial Differential Equations. 2022. Trends in Mathematics, Birkhäuser, Cham.. arXiv:2201.12336.
    Link

  88. 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.
    Link

  89. Barraza, E. Samuel., Cardona, D. On nuclear Lp multipliers associated to the harmonic oscillator, in:
    Analysis in Developing Countries, Springer Proceedings in Mathematics & Statistics, Springer, Imperial College London, UK, 2016. , M. Ruzhansky and J. Delgado (Eds), (2019). arXiv:1703.07453.
    Link

  90. 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. arXiv:1703.07453.
    Link

    Preprints

  91. Cardona, D., Martinez, M. A. Boundedness of pseudo-differential operators on the torus revisited, III. submitted. arXiv:2508.13338
    Link

  92. Cardona, D. Riesz-Means Bounds for Functional-Difference operators on mirror curves, submitted. arXiv:2508.07433.
    Link

  93. Cardona, D., Martinez, M. A. Boundedness of pseudo-differential operators on the torus revisited, II. submitted. arXiv:2505.01573
    Link

  94. Cardona, D., Delgado, J., Ruzhansky, M. Nuclearity, Schatten-von Neumann classes, distribution of eigenvalues and Lp-Lq-boundedness of Fourier integral operators on compact manifolds, submitted. arXiv:2408.06833.
    Link

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

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

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

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

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

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

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

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

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

  104. 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.
    Link

  105. 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.
    Link

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

 

 
 
 

Poster Vishvesh LpLq nonharmonic

Go back

Your message has been sent