Duván Cardona

 amspic
I am a current Ph.D. student at the Department of Mathematics: Analysis, Logic, and Discrete 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 talks and outreach activities are here.

  • 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.

The list of my publications:

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

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

  3. Cardona, D. Ruzhansky, M. [v1: Weak (1,1) continuity and Lp-theory for oscillating singular integral operators],[v2: Oscillating singular integral operators on graded Lie groups revisited], submitted.  arXiv:2201.12881

  4. Cardona, D.  The Wodzicki residue for pseudo-differential operators on compact Lie groups, submitted. arXiv:2201.12336

  5. 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

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

  7. Cardona, D., Ruzhansky, M. Sharpness of Seeger-Sogge-Stein orders for the weak (1,1) boundedness of Fourier integral operators., To appear in Archiv der Mathematik. arXiv:2104.09695 

  8. 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

  9. Cardona, D., Ruzhansky, M. Fourier multipliers for Triebel-Lizorkin spaces on compact Lie groups.,  Collect. Math. arXiv:2101.12314

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

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

  12. 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

  13. 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

  14. Cardona, D., Delgado, J., Ruzhansky, M. Determinants and Plemelj-Smithies formulas., submitted. arXiv:2012.13216

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

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

  17. 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

  18. 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.

  19. 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.

  20. 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

  21. 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

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

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

  24.  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

  25. 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.

  26. Cardona, D. The index of Toeplitz operators on compact Lie groups and simply connected closed 3-manifolds, submitted.

  27. 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

  28. Cardona, D. Messiouene, R.,  Senoussaoui, A.  Lp-bounds for  Fourier integral operators on the torus,  submitted, arXiv:1807.09892

  29. 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

  30. 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

  31.  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

  32. 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.

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

  34. 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.

  35. 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

  36. 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

  37. 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

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

  39. 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. httpsarXiv:1703.07453.

  40. 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).

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

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

  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 T^1 . J. Pseudo-Differ. Oper. Appl. Vol. 5 (4), 517-525,  (2014). 

Miscellaneous-Notes/Outreach activities.

 

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

  2. 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).

  3.  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).

  4. 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).

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

  6. 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

  7. 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).

  8. 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).

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

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

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

  12. Cardona, D. Invertibilidad de operadores pseudo-diferenciales definidos en Zn. Lect. Mat. Vol. 34 (2),  179-186, (2013)
  13. Cardona, D. Operadores pseudodiferenciales definidos en medidas de Borel, Rev. Integr. Temas Mat. Vol. 31 (1) , 25-42, (2013).

Duvan poster

Poster Vishvesh LpLq nonharmonic